14 GROUP ED—POSTTREATMENT BY EUROPLEXUS
ED.10
Object:
To posttreat a results file containing the EUROPLEXUS results
from a previously executed transient calculation.
Syntax :
1/ General syntax :
... title ...
<"ECHO">
<"OPNF" . . . >
"RESUL" . . .
<"DIME" . . . "TERM">
"SORT" $ "ARRET" . . . $
$ $
$ "FICHIER" . . . $
$ $
$ "ECRITURE" . . . $
$ $
$ "GRAPHIQUES" . . . $
$ $
$ ( "VISUALISER" . . . ) $
<"QUAL" . . . >
"FIN"
Comments:
These directives are described in detail on the following pages,
except for the QUAL directive, which has been already presented
on page I.25.
The following page shows a full synopsis of the EUROPLEXUS
posttreatment directives.
... title ...
<ECHO> <OPNF . . . >
RESU <FORM>
<SPLI> ALIC;ALIC TEMP;UNIV <CURR>;UNIV OBSO
nban;'nom_fich' <GARD> <PSCR>
<DIME <TIMP nimp> TERM>
<FONC ..., see page E.15>
SORT $ ARRE <TEMP time;NUPA npas;NSTO nsto> $
$ FICH <FORM> nfic $FREQ nfre;TFRE tfre $ $
$ $NUPA /LECT/;PASM pasm$ $
$ ECRI <COOR> <DEPL> <VITE> <ACCE> <FINT> <FEXT> $
$ <CONT> <EPST> <ECRO> /CTIM/ $
$ <NOPO;POIN /LECT/> <NOEL;ELEM /LECT/> $
$ <FICH <FORM> K200 ndca /CTIM/ POIN /LECT/ <CHAM>> $
$ GRAP AXTE coef 'nom_axe_Ox' $
$ <MINM> <FENE tmin tmax> $
$ <PERF 'nom_fic'> <PERK 'nom_fic'> $
$ (COUR nuco <'nomcourbe'> $
$ $WINT;WEXT;WCIN;BILA;WSUM;DTMI;DTMA;MXSU$ <COMP ico> $
$ $COOR;DEPL;VITE;ACCE$ $
$ $FORC;ADFT;MCPR;MCRO$ $
$ $MCTE;MCMF;SIGN;ECRN$ $
$ $LFNO;LFNV;ILNO;DTNO$ $COMP ico;NORM$ NOEU /LECT/ $
$ $CONT;ECRO;EPST;ENEL$ $
$ $WAUX;LFEL;LFEV;DTEL$ COMP ico <GAUS igau> ELEM /LECT/ $
$ $VCVI$ $COMP ico;NORM$ ELEM /LECT/ $
$ $SOMM nbrs*(courbe_i coef_i)$ $
$ $PROD pcoef nbrp*(courbe_k) $ $
$ $INTE courbe_i $ $
$ $DIST /LECT/ $ $
$ $LIBR $ $
$ $MASS;VOLU;BARY;VMOY$ $
$ $IMPU;ECIN;EINT;EEXT$ $
$ $EPDV;EINJ;RESU;IRES$ $
$ $ECRG;DT1 $ <COMP ico;NORM> <REGI nure>) $
$ (SCOU nuco <'nomcourbe'> <$T t;NPAS npas;NSTO nsto$> $
$ SAXE scoe 'nom_saxe' <INIT> /LECT/ $
$ $COOR;DEPL;VITE;ACCE$ $
$ $FORC;ADFT;MCPR;MCRO$ $
$ $MCTE;MCMF;SIGN;ECRN$ $
$ $LFNO;LFNV;ILNO;DTNO$ $COMP ico;NORM$ $
$ $CONT;ECRO;EPST;ENEL$ $
$ $WAUX;LFEL;LFEV;DTEL$ COMP ico <GAUS igau>) $
$ (RCOU nuco 'nomcourbe' FICH 'nom_fic' $
$ <RENA 'new_name'> <FACX fx> <FACY fy>) $
$ (DCOU nuco <'nomcourbe'> $npt*(x y);FONC ifon$) $
$ ($TRAC;XMGR$ $
$ $K200;LIST$ (nuco) <PS <TEXT>;MIF> AXES coef 'nom_axe_Oy' $
$ <XAXE nxax coex 'nom_axe_Ox'> $
$ <COLO (co)> <THIC (th)> <DASH (da)> $
$ <XZER> <YZER> <XGRD> <YGRD> <XLOG> <YLOG>) $
$ (VISU $T t;NPAS npas;NSTO nsto$ $
$ <PLAY> $
$ <sequel of interactive commands, see pages A.25, O.10> $
$ <ENDPLAY>) $
<QUAL ..., see page I.25>
FIN
14.1 TITLE AND CHOICE OF RESULTS FILE
ED.20
Object:
The user gives a title and specifies the
file (or files) from which the results to be edited will be read.
The file(s) must have been produced during a previous execution of EUROPLEXUS
(or during a previous phase of a composite execution, where the various
phases are separated by the keyword SUIT).
Currently, results may be edited from any of the following file types:

An ALICE file (either single or split);
 An ALICE TEMPS file;
 A file of type UNIVERSAL CURRENT;
 A file of type UNIVERSAL OBSOLETE.
 A file of type POCHHAMMER.
However, note that a file of type POCHHAMMER can only be read
in addition to a file of the other types (usually an ALICE file).
It cannot be read in by itself.
Syntax :
/TITLE/
<"ECHO">
<"OPNF" < "FORMAT" > nfic 'nom.fic'>
"RESUL" (<"FORMAT">
[ < "SPLI" > "ALIC" ; "ALIC" < "TEMP" > ; "POCH" ;
"UNIV" <"CURR"> ; "UNIV" "OBSO" ]
$[ nban ; 'nom_fich' ]$
<"GARDE">
<"PSCR"> )

"ECHO"


Like for a normal calculation, this keyword indicates that the
EUROPLEXUS input directives will be echoed in the execution window.
 "OPNF"


This option may be used to open the chosen results file, like for a normal
calculation. Refer to page A.28.
 "FORMAT"


This keyword indicates that the chosen results file is a formatted file.
By default, this file is unformatted.
 "SPLI"


The chosen results file is a set of ALICE split files rather than a single
file, produced by the directive ECRI ... FICH SPLI ALIC ...,
see page G.70.
 "ALIC"


The chosen results file is an ALICE file (this is the default).
 "ALIC TEMP"


The chosen results file is an ALICE TEMPS file.
 "POCH"


The chosen results file is a POCHHAMMER file (which is being read
in addition to another results file).
 "UNIV CURR"


The chosen results file is a file of type UNIVERSAL CURRENT.
The keyword CURR may be omitted in this case since this is the default
for a file of type UNIVERSAL.
 "UNIV OBSO"


The chosen results file is a file of type UNIVERSAL OBSOLETE.
 nban


Number of the logical unit on which the results file is
stored.
 nom_fich


Name of the results file, enclosed in single quotes.
 "GARDE"


This keyword allows to keep for the drawings the title read
in the results file. Else, it is the title defined above.
 "PSCR"


This keyword allows to produce the plots resulting
from the GRAP directive in PostScript. Since 1995
it is the default, so that this keyword id redundant now.
Comments:
The word RESULT is compulsory.
When it is present, only an edition of results may be done and not a normal
calculation.
14.2 DIMENSIONING
ED.30
Object :
Allocation of memory for the posttreatment of a results file
by means of EUROPLEXUS.
If one limits itself to graphical output,
EUROPLEXUS automatically allocates the necessary space, so it is
no longer necessary to give dimensions.
This directive must therefore be omitted in that case.
Syntax:
"DIME"
< "TIMP" nimp >
"TERM"

nimp


Number of time steps for which printing
on the listing is requested
(see option /CTIM/ of ECRI on page ED.50).
14.3 OUTPUTS
ED.40
Object :
The following directive enables the types of output
to be chosen.
Syntax:
"SORT"
$ "ARRET" <"TEMPS" time ; "NUPAS" npas ; "NSTO" nsto> $
$ $
$ "FICHIER" . . . $
$ $
$ "ECRITURE" . . . $
$ $
$ "GRAPHIQUES" . . . $
$ $
$ ( "VISUALISER" . . . ) $

ARRET


This directive allows to stop reading the results file at the time instant,
at the time step or at the time station corresponding to values
time
, npas
or nsto
, respectively,
specified in the directive, rather than reading the whole file.
Note that a storage station is always produces at step 0 (beginning
of the transient calculation): this storage station has the index nsto=0.
This directive is only useful for the qualification of a
calculation at intermediate times (and not at the final time as per default),
since it may not be combined with
the other directives FICH, ECRI,
GRAP and VISU, as indicated in the syntax.
For more details on the qualification, see directive QUAL on Page I.25.
 FICHIER


To extract from the chosen results file a certain number of computation
steps, and to store them in a new results file which will typically
contain less information (less storage stations).
 ECRI


To print out results on the EUROPLEXUS listing.
 GRAP


To produce graphic outputs. The curves of certain
variables are drawn with respect
to time or are printed on file(s) in a variety of possible formats.
 VISU


To produce (a subset of) the visualizations that are possible
during direct execution of the code (see Pages A.25 and O.10).
These include graphical rendering either interactively
in a window or in batch mode on a file and
production of animations.
Not all visualization types and features are available, though (see
below for details).
Comments:
The keyword SORT should appear only once in an input
data sequence. Note, however, that the VISU subdirective
may be repeated as many times as needed inside the SORT directive.
The directives ARRE, ECRI, GRAP, FICH and VISU
are mutually exclusive.
In the case that a graphical output is requested (GRAP ... TRAC),
the produced
file is in the PostScript format (a product of Adobe Co.).
14.4 CREATING A REDUCED RESULTS FILE
ED.45
Object:
To extract a certain number of computation steps from the chosen
results file, in order to create a new results file which has the same
structure as if it was created directly, but typically contains less
information (less storage stations).
Syntax:
"FICHIER" < "FORMAT" > nfic [ "FREQ" nfreq ;
"TFREQ" tfreq ;
"NUPAS" /LECTURE/ ;
"PASMAX" pasmax ]

FORMAT


This keyword indicates that the new file created will be formatted.
By default, it is unformatted.
 nfic


Logical number of the new file.
 nfreq


All the results whose step number is a multiple of nfreq are
extracted from the results file.
 tfreq


Time interval between two extracted results.
 /LECTURE/


List of the step numbers to be taken.
 pasmax


Maximum number of the time step to be copied.
Comments:
The options FREQ, TFREQ, NUPAS and PASMAX
can be combined.
If the step number required is not stored in file nfic, EUROPLEXUS
takes the step just above it.
The option PASMAX allows e.g. to “clean up” a results file that has
become unusable due to a computation error. In fact, one
may then create a new file containing the results of the steps
from the beginning to a step pasmax prior to the encountered error.
Warning:
The logical unit number of the new file (nfic) must be different
from that of the old one, nban, defined in the instruction RESULT
(see page ED.20).
14.5 PRINTOUTS ON THE LISTING
ED.50
Object :
To print data extracted from a chosen results file onto the EUROPLEXUS listing
file or to produce a CASTEM 2000 file for further postprocessing
by CASTEM 2000.
Syntax :
"ECRITURE"
< "COOR" > < "DEPL" > < "VITE" > < "ACCE" >
< "FINT" > < "FEXT" > < "FLIA" >
< "CONT" > < "EPST" > < "ECRO" >
< "ENER" > < "MCVA" > < "MCVC" >
< "MCVS" > < "FAIL" > < "VFCC" >
/CTIM/
$[ "NOPOINT" ; "POINT" /LECTURE/ ]$
$[ "NOELEM" ; "ELEM" /LECTURE/ ]$
< "FICHIER" < FORMAT > "K2000" ndcast /CTIM/
"POINT" /LECTURE/
< "CHAMELEM" > >

"COOR"


Coordinates are printed on the EUROPLEXUS listing.
 "DEPL"


Displacements are printed on the EUROPLEXUS listing.
 "VITE"


Velocities are printed on the EUROPLEXUS listing.
 "ACCE"


Accelerations are printed on the EUROPLEXUS listing.
 "FINT"


Internal forces are printed on the EUROPLEXUS listing.
 "FEXT"


Total external forces are printed on the EUROPLEXUS listing.
 "CONT"


Stresses are printed on the EUROPLEXUS listing.
 "EPST"


Total strains are printed on the EUROPLEXUS listing.
 "ECRO"


Hardening parameters are printed on the EUROPLEXUS listing.
 "ENER"


Energies are printed on the EUROPLEXUS listing.
 "MCVA"


Printout of nodal quantities related to multicomponent fluids:
pressure, density, temperature, sound speed and mass fractions.
Note that this type of printout is incompatible with MCVC
and MCVS.
 MCVC


Printout of conserved variables (nodal quantities) related to
multicomponent fluids: partial densities (ρ_{i})
of the various components i, momentum (ρ u)
(each spatial component separately), energy (ρ E).
Note that this type of printout is incompatible with MCVA.
 MCVS


Printout of secondary variables (nodal quantities) related to
multicomponent fluids: total density (ρ), total pressure p,
sound speed c, pressure derivative (∂ p/∂ (ρ e)),
absolute temperature (T),
pressure derivative (∂ p/∂ (ρ_{i})) for each component,
mass fraction (µ_{i}) for each component.
Note that this type of printout is incompatible with MCVA.
 "FAIL"


Failure values are printed on the EUROPLEXUS listing.
 VFCC


Printout at each selected output time of “element” quantities
related to cellcentred Finite Volumes:
various volumerelated quantities and conserved variables.
 /CTIM/


Reading procedure of the chosen time instants at which the
results have to be printed on the listing. See page INT.57.
 "NOPOINT"


Do not print any nodal variables. By default the chosen nodal variables
are printed for all nodes stored in the results file.
 "POINT /LECTURE/"


Print the chosen nodal variables only for the nodes defined in
the /LECT/ (provided they are stored in the results file).
 "NOELEM"


Do not print any element variables. By default the chosen element variables
are printed for all elements stored in the results file.
 "ELEM /LECTURE/"


Print the chosen element variables only for the elements defined in
the /LECT/ (provided they are stored in the results file).
 "FICH"


Produce a CASTEM 2000 results file from the EUROPLEXUS results file.
 "FORMAT"


If this keyword is present, the CASTEM 2000 results file is formatted; else,
it is unformatted (binary).
 ndcast


Logical unit number of the CASTEM 2000 file; the results file is
written with the standard SAUVER format of CASTEM 2000.
It may be read by CASTEM 2000 by using the command RESTITUER.
It is mandatory to specify the list of points for which results
have to be included in the file, and if necessary also
the word CHAMELEM.
 /CTIM/


Reading procedure of the chosen time instants at which the
results have to be stored. See page INT.57.
 "POIN" /LECTURE/


List of the nodes for which the results are stored
for a subsequent postprocessing by CASTEM 2000.
This directive is mandatory for a file of type "K2000".
 "CHAMELEM"


This keyword causes the CHAMELEMS to be included in the CASTEM 2000
file. If it is omitted, the latter will only contain
the selected CHAMPOINTS, on the nodes identified by
the previous directive POINT.
Comments :
The syntax is the same as for directive ECRI. For more
details see page G.10 and following ones.
14.6 GRAPHIC OUTPUTS
ED.60
Object :
To produce drawings or lists on files (in a variety of formats)
of different quantities in the form of curves with respect
to time, or with respect to a curvilinear abscissa, or combined plots
(e.g. sigma/epsilon graphs).
Syntax:
"GRAP" "AXTEMP" coef 'nom_axe_Ox'
< "MINMAX" >
< "PERFO" 'nom_fic' >
< "PERK" 'nom_fic' >
< "FENETRE" tmin tmax >
( "COURBE" . . . )
( "SCOURBE" . . . )
( "RCOURBE" . . . )
( "DCOURBE" . . . )
( "PCOURBE" . . . )
( "TRACE" . . . )
( "XMGR" . . . )
( "K2000" . . . )
( "LISTE" . . . )
( "FVAL" . . . )

coef


The time values are multiplied by coef (this e.g. enables
the unit of measure to be changed).
 ’nom_axe_Ox’


Name of the time axis (at most 16 characters), enclosed
in apostrophes.
 MINMAX


Print on the EUROPLEXUS listing the minimum and the maximum
values for each curve.
 PERFO


The value tables specified in the following LISTE directive will be
output on an auxiliary file, whose name by default is <base>.PUN,
where <base> is the base name of the current calculation.
This directive allows to change the default name into the following
’nom_fic’.
 PERK


The value tables specified in the following K2000 directive will be
output on an auxiliary file, whose name by default is <base>.PUK,
where <base> is the base name of the current calculation.
This directive allows to change the default name into the following
’nom_fic’.
 FENETRE


Only the results in a given time interval (time window) are considered.
 tmin


Minimum time (beginning of the time window).
 tmax


Maximum time (end of the time window).
 COURBE


Define a curve representing the evolution in time
of a certain variable in the current transient calculation.
See below for the full details of this directive.
 SCOURBE


Define a curve representing the evolution in space
of a certain variable in the current transient calculation.
The space is a curvilinear abscissa (s) defined by a sequence of nodes.
The curve is by default built at the final time of the current calculation.
To select a different time, use the ARRET directive described on
page ED.40.
See below for the full details of this directive.
 RCOURBE


Read in a curve representing the evolution in time or in space
of a certain variable in a previously executed EUROPLEXUS calculation.
The data are read in from a “punch” file produced by EUROPLEXUS via the
SORT LIST directive, to be described below.
In this way, results from different EUROPLEXUS runs may be compared
on the same plot.
See below for the full details of this directive.
 DCOURBE


Define a curve in the form of a table of (x, y) values.
This allows e.g. to build a piecewise analytical solution to be compared with
numerical results. It may even be used to input experimental results to
be used as a reference solution.
See below for the full details of this directive.
 PCOURBE


Define a set of curves for PochhammerChree postprocessing.
See below for the full details of this directive.
 TRACE


Produce a graph containing one or more of the curves defined above,
plotted either versus time, or versus space (curvilinear abscissa), or
as a function of another curve (e.g. σє type of plot).
The graph is produced in the PostScript language on a file.
 XMGR


Same as TRACE but the graph data are stored on a file which may then
be read by the XMGR program (a publicly available software) to produce
the actual drawing.
 K2000


Same as TRACE but the graph data are stored on a file which may then
be read by the CASTEM 2000 program to produce the actual drawing.
 LISTE


Same as TRACE but the graph data are stored on a file which may then
be read by a generic external tool to produce the actual drawing.
The file format is very simple.
This command also allows to store a curve in a certain EUROPLEXUS run
and read it in (by the RCOURBE directive described above) in a
subsequent EUROPLEXUS run, thus opening the way to the production
of graphs containing comparisons of results from different EUROPLEXUS
calculations, and even analytical curves or experimental data.
 FVAL


Find values (abscissas) x of a curve for which the curve assumes
a given value v, i.e. for which y(x)=v. Linear interpolation
is used.
Comments:
 The time axis is the same for all drawings produced as a function of time.
 The time window is the same for all drawings produced as a function of time.
Example :
"GRAP" "AXTEMP" 1000. 'TEMPS (MS)'
"FENETRE" 0. 10E3 MINMAX
. . .
14.6.1 Postprocessing in adaptivity
ED.65
The postprocessing of results in mesh adaptive computations may
be somewhat different from the case of normal computations with
a constant mesh connectivity. Some care is required in the
interpretation of mesh adaptive results, especially as concerns
time curves in selected nodes or elements.
The visualization of maps of values at a fixed time, e.g. a
pressure field in the form of isovalues or a velocity field
in the form of vectors, is similar to the case of nonadaptive
calculations. The only thing to keep in mind is that, if a zone or part of
the mesh must be selected for visualization, then the user
should normally provide the list of the base elements. The code will
then automatically replace these elements by the set of their
active descendants at the chosen time. This mechanism is transparent to
the user since object names and element group names always contain
the indexes of the base elements concerned. Therefore, if no element
indexes are explicitly given, the procedure from the user’s viewpoint
is exactly like in the case of nonadaptive computations.
The production of time curves in adaptive computations requires some more
attention, since an element or node at which the results are to
be extracted must be specified and this can be either a base item
or a descendant item. Furthermore, the element or node can be active only
during part of the time transient.
The following rules are applied:
Rule 1: in an adaptive calculation, a noderelated quantity

represents the value belonging to the node itself, if the node
is currently used. Note that in adaptivity nodes can be either used or unused.
A used node is also active. An unused node is inactive. Base nodes
are always used and therefore they are always active.
 is undefined (and is typically set to 0.0) if the node is
currently not used.
Rule 2: in an adaptive calculation, an elementrelated quantity

represents the value belonging to the element itself, if the element
is currently active.
 represents the weighted average value of all its current
active descendants, if the element is currently used but inactive.
Note that, in particular, base elements (unlike base nodes)
can become inactive, although they are always used.
 is undefined (and is typically set to 0.0) if the element is
currently not used.
Rule 3: in an adaptive calculation, a list of elements or
the name of an object or group made of elements

represents the listed elements themselves,
if such elements are currently active.
 represents the set of all current active descendants of the
elements listed, if the elements are currently used but inactive.
 is illegal if the elements listed are currently not used.
14.6.2 Curve (Nodal Variables)
ED.70
Object:
Definition of the variables relative to nodes to be drawn or listed.
Syntax :
"COURBE" nuco < 'nomcourbe' >
[ "COOR" ; "DEPL" ; "VITE" ; "ACCE" ; "FINT" ; "FEXT" ;
"FLIA" ; "ADFT" ; "MCPR" ; "MCRO" ; "MCTE" ; "MCMF" ;
"MCUX" ; "MCUY" ; "MCUZ" ; "SIGN" ; "ECRN" ; "LFNO" ;
"LFNV" ; "ILNO" ; "DTNO" ; "VITG" ; "NTLE" ; "MASN" ;
"FDEC" ; "PFSI" ; "PFMI" ; "PFMA" ]
[ "COMP" icomp ; "NORME" ]
$[ "NOEU" /LECTURE/ ;
"ZONE" /LECTURE/ ;
"POSI" $[ x y <z> ;
"FOLL" dx dy <dz> /LECT1/ ]$
"OBJE" /LECT2/ ]$

nuco


Identifier of the curve (reference for TRAC, XMGR, K2000
or LISTE).
A (unique) integer number, freely chosen by the user, by which the curve
may be successively referred to when needed.
 ’nomcourbe’


Name of the curve (reference for the user). This will appear on plots, etc.
 COOR


Coordinate.
 DEPL


Displacement.
 VITE


Velocity.
 ACCE


Acceleration.
 FINT


Internal force.
 FEXT


Total external force.
 FLIA


External force due to coupled links (LINK COUP).
 ADFT


Advectiondiffusion temperature.
 MCPR


Finite volume (MC) pressure.
 MCRO


Finite volume (MC) density.
 MCTE


Finite volume (MC) temperature.
 MCMF


Finite volume (MC) component mass fraction.
 MCUX


Finite volume (MC) fluid velocity along X computed
from the conserved variable (u_{x} = (ρ u_{x}) / ρ)).
 MCUY


Finite volume (MC) fluid velocity along Y computed
from the conserved variable (u_{y} = (ρ u_{y}) / ρ)).
 MCUZ


Finite volume (MC) fluid velocity along Z computed
from the conserved variable (u_{z} = (ρ u_{z}) / ρ)).
 SIGN


Spectral element stress.
 ECRN


Spectral element internal variable.
 LFNO


Logarithm in base 2 of the
level factor associated with a node
in the spatial time step partitioning algorithm.
 LFNV


Logarithm in base 2 of the
level factor associated with a node, including the neighbours
in the spatial time step partitioning algorithm.
 ILNO


Flag indicating whether a node is (1) or is not (0) subjected
to a link condition, used
in the spatial time step partitioning algorithm.
 DTNO


Stability time step associated with a node, used
in the spatial time step partitioning algorithm.
 VITG


Grid velocity (ALE only).
 NTLE


Node tree level (only in adaptivity).
 MASN


Nodal mass.
 FDEC


External force due to decoupled links (LINK DECO).
 PFSI


Overpressure due to FSI in the nodes of CLxx elements associated with
an IMPE VISU material (see Page C.885) and with either
COUP or DECO specified. These CLxx elements, used only
for results visualization purposes, must be attached
to structural elements (typically shells) embedded in a fluid and
subjected to either FLSR or FLSW model of FSI.
 PFMI


Minimum FSI overpressure in time at the node (see PFSI above.
 PFMA


Maximum FSI overpressure in time at the node (see PFSI above.
 COMP


Introduces the chosen component.
 icomp


Component number. Default value is 1.
 NORM


The norm of the considered vector (where applicable) is drawn.
 NOEU /LECTURE/


Number of the node. The procedure /LECTURE/ allows if necessary
to read a GIBI object, of which only the first node will be retained.
 ZONE /LECTURE/


Set of nodal numbers defining a zone. The contributions of all these nodes
are added together. This probably makes sense only for some types of
variables (e.g. forces, masses etc.). This can be useful to plot
e.g. the total (resultant) force acting on a set of nodes, or the total
mass of such nodes. It is an alternative to the use of the REGI
directive. The difference is that with REGI the region must be
defined in the main calculation, and it cannot be defined when reading
the results file (e.g. an Alice file). The present ZONE directive,
on the contrary, can be defined “on the fly” when reading any results
file (provided this file contains the results of all concerned nodes).
 POSI


The nodal values should be extracted at the nearest node to the position
specified next. Note that the nearest node may vary in time, either due to
motion of the mesh or to mesh adaptivity. The position can either be specified
by its coordinates (and in this case it is fixed in time), or by
an offset to the position of a node in the mesh. In the latter case, if
the specified node moves in time, then the position moves as well
by “following” the specified node. This may be useful to track, say,
the fluid velocity at a position slightly upstream of a deformable plate.
 x y <z>


Coordinates of the position (fixed in time).
 FOLL /LECT1/


The position should follow the node specified in the /LECT1/.
 dx dy <dz>


Offset of the position with respect to the node.
 OBJE /LECT2/


Object (list of elements) whose nodes
are candidates for the search of the nearest node.
If more than one node has the minimum distance from the position specified,
then the first such node is retained.
Note that although the variable to be drawn is relative to nodes,
the object must be defined in term of (base) elements. The code then extracts
automatically the nodes belonging to such elements (or to their
active descendants, in case of adaptivity).
Comments :
The directive COURBE can be repeated as many times as desired,
but each time with a different identifier.
Curve identifiers may be freely chosen by the
user, and the order in which they are given is irrelevant.
The keyword FORC is accepted as a synonym of FEXT
for backward compatibility, but
is obsolescent and should not be used in new input files.
For an introduction to postprocessing, and in particular to
time curves production in mesh adaptive calculations, see
page ED.65.
14.6.3 Curve (Element Variables)
ED.80
Object:
Definition of the variables relative to elements to be drawn or listed.
Syntax:
"COURBE" nuco < 'nomcourbe' >
[
[ "CONT" ; "ECRO" ; "EPST" ; "ENEL" ; "WAUX" ; "LFEL" ;
"LFEV" ; "DTEL" ; "ELCE" ; "FAIL" ; "RISK" ; "CERR" ;
"MAXC" ; "ERRI" ; "CLEN" ; "ILEN" ; "ETLE" ; "MASE" ]
"COMP" icomp $[ "GAUS" igaus ; "GAUZ" igauz ]$ ;
"VCVI" [ "COMP" icomp ; "NORM" ]
]
$[ "ELEM" /LECTURE/ ;
"ZONE" /LECTURE/ ;
"POSI" $[ x y <z> ;
"FOLL" dx dy <dz> /LECT1/ ]$
"OBJE" /LECT2/ ]$

nuco


Identifier of the curve (reference for TRAC, XMGR, K2000
or LISTE).
A (unique) integer number, freely chosen by the user, by which the curve
may be successively referred to when needed.
 ’nomcourbe’


Name of the curve (reference for the user). This will appear on plots, etc.
 CONT


Stress tensor.
 ECRO


Hardening quantity.
 EPST


Total deformation tensor.
 ENEL


Internal energy.
 WAUX


Auxiliary energy terms for the element (see details below).
 LFEL


Logarithm in base 2 of the
level factor associated with an element in the spatial time step
partitioning algorithm.
 LFEV


Logarithm in base 2 of the
level factor associated with an element including its neighbours
in the spatial time step partitioning algorithm.
 DTEL


Stability time step Δ t_{stab} associated with the element.
The stability step is the critical
step Δ t_{crit} estimated by the code (roughly the element length
L divided by the speed of sound c in the element material)
multiplied by the safety coefficient φ (CSTA,
by default 0.8):
Δ t_{stab}=φΔ t_{crit}≈φL/c.
 ELCE


Coordinates of the barycentre of the element.
 FAIL


Failure level of the element.
 RISK


Risk level of the element (only if risk is activated).
COMP must be given to define the kind of risk:
COMP=1 chooses the risk of eardrum rupture,
COMP=2 chooses the risk of death.
Be aware that when reading results from an Alice file (produced by a
previous calculation with risk activation), it is mandatory to
(re)specify the whole RISK directive (in particular as concerns the
PROB ... and LUNG ... sub directives, see page A.30),
because the risk
is computed with the current values of the optional parameters.
 CERR


Constant used in element error indicator calculation (adaptivity),
see the CERR input keyword of the ADAP directive on page B.210.
 MAXC


Maximum principal curvature of leastsquares fitting function,
used for element error indicator calculation (adaptivity).
 ERRI


Element error indicator (adaptivity).
 CLEN


Current characteristic element length
used in element error indicator calculation (adaptivity).
 ILEN


Optimal (indicated) characteristic element length
resulting from error indicator calculations (adaptivity).
 ETLE


Element tree level (adaptivity).
 MASE


Element mass.
 VCVI


Material or particle velocity (first idim components) in Finite Volumes
Cell Centred model. Note that these vectors are not represented at the
nodes but at the “elements” (i.e. Finite Volumes) centroids.
 COMP


Introduces the component (unused for ENEL, LFEL, LFEV
and DTEL).
 icomp


Number of the component.
 GAUS


Allows to choose a specific Gauss point index (only for the quantities
CONT, EPST and ECRO).
 igaus


Number of the Gauss point chosen. The special value 0 means that
the average over all Gauss points in the element is taken.
The default value is 1, i.e. if neither GAUS nor GAUZ
is specified then the first Gauss Point of the specified element is
taken. Note that this default is different from the default in
rendering via OpenGL, where 0 (average over all Gauss Points) is assumed.
 GAUZ


Allows to choose a specific “lamina” of the (shell) element.
The value is the index of the lamina through the thickness
(only for the quantities
CONT, EPST and ECRO).
In this case, the code takes the average value of all Gauss Points
belonging to the specified lamina.
 igauz


Number of Gauss point through the thickness (i.e. index of the chosen
lamina).
 NORM


The norm of the VCVI vector is drawn.
 ELEM /LECTURE/


Number of the element. The procedure /LECTURE/ allows if necessary
to read a GIBI object, of which only the first element will be retained.
 ZONE /LECTURE/


Set of element numbers defining a zone. The contributions of all these elements
are added together. This probably makes sense only for some types of
variables (e.g. masses). This can be useful to plot
e.g. the total (resultant) mass of a set of elements.
It is an alternative to the use of the REGI
directive. The difference is that with REGI the region must be
defined in the main calculation, and it cannot be defined when reading
the results file (e.g. an Alice file). The present ZONE directive,
on the contrary, can be defined “on the fly” when reading any results
file (provided this file contains the results of all concerned elements).
 POSI


The element values should be extracted
at the nearest element (centroid) to the position
specified next. Note that the nearest element may vary in time, either due to
motion of the mesh or to mesh adaptivity. The position can either be specified
by its coordinates (and in this case it is fixed in time), or by
an offset to the position of a node in the mesh. In the latter case, if
the specified node moves in time, then the position moves as well
by “following” the specified node. This may be useful to track, say,
the fluid pressure at a position slightly upstream of a deformable plate.
 x y <z>


Coordinates of the position (fixed in time).
 FOLL /LECT1/


The position should follow the node specified in the /LECT1/.
 dx dy <dz>


Offset of the position with respect to the node.
 OBJE /LECT2/


Object (list of elements) whose elements
are candidates for the search of the nearest element.
If more than one element has the minimum (centroid)
distance from the position specified,
then the first such element is retained.
Note that
the object must be defined in term of (base) elements. The code then extracts
automatically the list of their
active descendants, in case of adaptivity.
Comments:
The directive COURBE can be repeated as many times as desired,
but each time with a different identifier.
Curve identifiers may be freely chosen by the
user, and the order in which they are given is irrelevant.
If the keyword GAUSS is omitted, the first integration
point is considered. If GAUSS is set to 0, the average
over all integration points is used.
As concerns the auxiliary energy terms for the element (WAUX),
the following components are available at the moment:

WAUX 1 ⇒ Energy dissipated by artificial viscosity (WARD)
 WAUX 2 ⇒ Pressure work for fluids −PdV (W_PDV)
 WAUX 3 ⇒ Energy injected or lost at the walls (W_INJ)
 WAUX 4 ⇒ Kinetic energy for CCFV Elements on X axis
 WAUX 5 ⇒ Kinetic energy for CCFV Elements on Y axis
 WAUX 6 ⇒ Kinetic energy for CCFV Elements on Z axis
 WAUX 7 ⇒ Total Energy for CCFV Elements
 WAUX 8 ⇒ Used for saving initial injected energy
 WAUX 9 ⇒ Total energy of the liquid phase (Only ADCR/ADCJ Model)
 WAUX 10 ⇒ Total energy of the bubble (Only ADCR/ADCJ Model)
 WAUX 11 ⇒ Total energy of the cover gas (Only ADCR/ADCJ Model)
 WAUX 12 ⇒ Kinetic energy of the liquid phase (Only ADCR/ADCJ Model)
 WAUX 13 ⇒ Kinetic energy of the bubble (Only ADCR/ADCJ Model)
 WAUX 14 ⇒ Kinetic energy of the cover gas (Only ADCR/ADCJ Model)
 WAUX 15 ⇒ Internal energy of the liquid phase (Only ADCR/ADCJ Model)
 WAUX 16 ⇒ Internal energy of the bubble (Only ADCR/ADCJ Model)
 WAUX 17 ⇒ Internal energy of the cover gas (Only ADCR/ADCJ Model)
Quantities 4 to 17 were added to account for auxiliary energies needed in FV cases.
Contrary to FE, Total and kinetic energy FV contributions have to be computed
at elements and not at nodes.
Quantities 9 to 17 are only relevant for the ADCR/ADCJ Model, it will return 0 in other cases.
Note:
All printed energy quantities are equivalent
in FE and FV cases, except forW_PDV : In FE, the contribution of pressure work W_PDV
on the variation of kinetic energy is neglected in relation to the internal energy variation,
which is relevant for smooth solutions. In FV, W_PDV is computed as the variation of total energy,
which is always the work of pressure forces for a standalone domain.
For an introduction to postprocessing, and in particular to
time curves production in mesh adaptive calculations, see
page ED.65.
14.6.4 Curve (Combinations)
ED.90
Object:
Definition of combinations of the previously defined curves, to
be drawn or listed.
Syntax:
"COURBE" nuco < 'nomcourbe' >
[ "SOMME" nbrs*( courbe_i coef_i ) ;
"PRODUIT" pcoef nbrp*( courbe_k ) ;
"INTEGRALE" courbe_i ;
"DISTANCE" /LECTURE/ ;
"LIBR" ;
"ADDC" icou val ; "SUBC" icou val ;
"MULC" icou val ; "DIVC" icou val ;
"EXPC" icou val ; "CEXP" icou val ;
"SHIFT" icou val ; "MOVE" icou ival ;
"ADD" icou jcou ; "SUB" icou jcou ;
"MUL" icou jcou ; "DIV" icou jcou ;
"EXPF" icou jcou ; "DUP" icou jcou ;
"ABS" icou ; "SEGN" icou ;
"SQRT" icou ; "INV" icou ;
"EXP" icou ; "LN" icou ;
"LOG10" icou ; "SIN" icou ;
"COS" icou ; "ASIN" icou ;
"ACOS" icou ; "DIFF" icou ;
"INT" icou ; "AVER" icou ;
"MAX" icou ; "MIN" icou ;
"MEAN" nc*(icou) ; "SMAX" nc*(icou) ;
"SMIN" nc*(icou) ; "JOIN" nc*(icou) ;
"FILT" "MOYG" icou nval ]

nuco


Identifier of the curve (reference for TRAC, XMGR, K2000
or LISTE).
A (unique) integer number, freely chosen by the user, by which the curve
may be successively referred to when needed.
 ’nomcourbe’


Name of the curve (reference for the user). This will appear on plots, etc.
 SOMME


The current curve results from the linear combination
of nbrs curves, among those already defined.
result = coef\_1*courbe\_1 ... + coef\_i*courbe\_i + ...

PRODUIT


The current curve results from the product
of nbrp curves, among those already defined.
result = pcoef * courbe\_1 ... *courbe\_k * ...
 INTEGRALE


Each point of this curve is the value at time t of the
integral between 0 and t of curve number courbe_i, supposed
already defined.
 DISTANCE


The current curve results from the calculation of the
distance between the two nodes specified by the
following directive /LECTURE/.
 LIBR


The variable concerned by this curve is computed by
the subroutine GRLIBR, written by the user.
 ADDC


Add to curve icou a constant value val.
 SUBC


Subtract from curve icou a constant value val.
 MULC


Multiply curve icou by a constant value val.
 DIVC


Divide curve icou by a constant value val.
 EXPC


Raise curve icou to a constant power val.
 CEXP


Raise constant val to power values in curve icou (powers
of a constant).
 SHIFT


Translate of curve icou in its abscissa by a value val.
Undefined values are set to zero. The abscissa of the generated
curve is the same as that of curve icou.
 MOVE


Translate of curve icou in its abscissa by a value val.
The abscissa of the generated curve is no longer
the same as that of curve icou, but it is shifted by the
chosen amount val.
 ADD


Add curve jcou to curve icou.
 SUB


Subtract curve jcou from curve icou.
 MUL


Multiply curve icou by curve jcou.
 DIV


Divide curve icou by curve jcou.
 EXPF


Raise curve icou to power values contained in curve jcou.
 DUP


Copy of curve icou having the abscissa of curve jcou.
The result is set at zero in the nonoverlapping abscissa zones.
 ABS


Absolute value of curve icou.
 SEGN


Sign (unit) function of curve icou.
 SQRT


Square root of curve icou.
 INV


Inverse of curve icou.
 EXP


Exponential of curve icou.
 LN


Natural logarithm of curve icou.
 LOG10


Decimal logarithm of curve icou.
 SIN


Sine of curve icou.
 COS


Cosine of curve icou.
 ASIN


Arc sine of curve icou.
 ACOS


Arc cosine of curve icou.
 DIFF


Derivative of curve icou with respect to its abscissa (usually time).
 INT


Integral of curve icou with respect to its abscissa (usually time).
 AVER


Average value of curve icou. This results in a
single value, repeated over the whole abscissa.
 MAX


Maximum value of a curve icou. This results in a
single value, repeated over the whole abscissa.
 MIN


Minimum value of a curve icou. This results in a
single value, repeated over the whole abscissa.
 MEAN


Arithmetic mean of a set of nc curves icou.
 SMAX


Upper bound of a set of nc curves icou.
 SMIN


Lower bound of a set of nc curves icou.
 JOIN


Union of a set of nc curves icou.
The values from each curve are merged together to form
a new curve. This especially makes sense for
“curves” consisting of just one point each,
or for curves whose definition domains are disjoint.
 FILT MOYG


Mobile average on nval consecutive values of curve icou .
Comments:
The directive COURBE can be repeated as many times as desired,
but each time with a different identifier.
Curve identifiers may be freely chosen by the
user, and the order in which they are given is irrelevant.
For SOMME and PRODUIT, the curves starting
from which the sum (resp. product) is computed must
have identifiers lower than that of the current curve
and must have been already defined.
Commands ADDC to SMIN have been inspired from
similar ones present in the TPLOT data management system, developed
at JRC since the 1970’s.
For these commands, the curves identified by icou,
jcou, etc.,
must have been already defined.
Note also that for any of these commands that involve two or
more curves icou, jcou, etc., with the notable
exception of the DUP command, the abscissas (i.e. the
discrete xvalues) of all such curves must be identical,
otherwise the combination may not be computed.
Note also that, with respect to TPLOT, the meanings of MIN, SMIN
and of MAX, SMAX have been interchanged.
Moreover, MIN and MAX now produce a (uniformvalued)
curve rather than the printout of a single value.
The subroutine GRLIBR allows to compute a quantity
as a function of other quantities defined previously by a directive
COURBE.
An example of such subroutine is:
Programming example for GRLIBR:
SUBROUTINE GRLIBR(TT,VAL,NT,NTEMAX)
C
C
C CALCUL LIBRE DE GRANDEURS A TRACER EN FONCTION DU TEMPS
C
C
C TT = TABLEAU DES TEMPS (BANDE ALICE)
C IT = NUMERO DU PAS DE TEMPS
C NT = NOMBRE DE PAS DE TEMPS TOTAL (BANDE ALICE)
C ICO = NUMERO D'UNE COURBE
C VAL(IT,ICO) = TABLEAU DES GRANDEURS DEFINIES PAR UNE COURBE
C NTEMAX = NOMBRE MAXIMAL DE POINTS
C
REAL TT, VAL
DIMENSION TT(NTEMAX),VAL(NTEMAX,*)
C
C EXEMPLE : A = B * C
C DO 10 IT=1,NT
C 10 VAL(IT,5)=VAL(IT,1)*VAL(IT,3)
C
C EXEMPLE d'INTEGRATION :
C VAL(1,40)=0.
C NT1=NT1
C DO 10 IT=1,NT1
C 10 VAL(IT+1,40)=VAL(IT,40)+0.5*(VAL(IT+1,22)+VAL(IT,22))
C * *(TT(IT+1)TT(IT))
RETURN
END
Warning: the tables TT and VAL must be in simple precision
(R*4).
14.6.5 Curve (Regional Balances)
ED.100
Object:
Definition of quantities related to regions to be drawn or listed.
Syntax:
"COURBE" nuco < 'nomcourbe' >
[ "MASS" ; "VOLU" ; "BARY" ; "VMOY" ; "VEMX" ; "VEMN" ; "DMOY" ;
"DIMX" ; "DIMN" ; "AMOY" ; "ACMX" ; "ACMN" ; "IMPU" ; "ECIN" ;
"EINT" ; "EEXT" ; "EPDV" ; "EINJ" ; "RESU" ; "IRES" ; "ECRG" ;
"ECRM" ; "EMAS" ; "FLIR" ; "RRIS" ; "EPSM" ; "NERO" ; "NEND" ;
"CERO" ; "CEND"]
$[ "COMP" icomp ; "NORM" ]$
"REGION" nureg

nuco


Identifier of the curve (reference for TRAC, XMGR, K2000
or LISTE).
A (unique) integer number, freely chosen by the user, by which the curve
may be successively referred to when needed.
 ’nomcourbe’


Name of the curve (reference for the user). This will appear on plots, etc.
 MASS


Mass of the region (scalar, computed via XMEL).
 VOLU


Volume of the region (scalar).
 BARY


Barycenter of the region (vector).
 VMOY


Mean velocity of the region (vector).
 VEMX


Maximum velocity (absolute) of the region (vector), only components 1 to 3.
 VEMN


Minimum velocity (absolute) of the region (vector), only components 1 to 3.
 DMOY


Mean displacement of the region (vector).
 DIMX


Maximum displacement (absolute) of the region (vector), only components 1 to 3.
 DIMN


Minimum displacement (absolute) of the region (vector), only components 1 to 3.
 AMOY


Mean acceleration of the region (vector).
 ACMX


Maximum acceleration (absolute) of the region (vector), only components 1 to 3.
 ACMN


Minimum acceleration (absolute) of the region (vector), only components 1 to 3.
 IMPU


Impulse (momentum) of the region (vector).
 ECIN


Kinetic energy of the region (vector).
 EINT


Internal energy of the region (scalar).
 EEXT


Work of external forces applied to the region (scalar).
 EPDV


Work of pressure forces (PdV) for the region (scalar).
 EINJ


Energy injected in the region (scalar).
 RESU


Resultant of the external forces applied to the region (vector).
 IRES


Impulse due to external forces applied to the region (vector).
 ECRG


Sum of the values of ECR on the Gauss points of the region
(vector without norm).
 ECRM


Average of the ECR over the region.
 EMAS


Mass of the region (scalar, computed via the element masses XM0).
 FLIR


Resultant of the force due to LINK/LIAI applied at the nodes.
 RRIS


Average of the RISK over the region.
 EPSM


Average of the EPST over the region.
 NERO


Number of eroded elements over the region (See G.100).
 NEND


Number of damaged elements over the region (See G.100).
 CERO


Number of eroded classes over the region (See G.100).
 CEND


Number of damaged classes over the region (See G.100).
 COMP


Introduces the component.
 icomp


Index of the component.
 NORME


The norm of the chosen vector will be plotted.
 nureg


Number of the concerned region in the order of definition.
Comments:
The directive COURBE can be repeated as many times as desired,
but each time with a different identifier.
Curve identifiers may be freely chosen by the
user, and the order in which they are given is irrelevant.
The directives COMP and NORM make sense only for vectors: they
are possible with BARY, DIMX, DIMN, VMOY, VEMX,
VEMN, IMPU, ECIN, RESU, and IRES. Furthermore,
NORM does not make sense for ECRG, ECRM, EPSM and
RRIS (only COMP is possible).
The directives COMP and NORM make no sense for scalars:
MASS, VOLU, EINT, EEXT, EPDV, EINJ,
EMAS, NERO, NEND, CERO and CEND.
If the keyword COMP is absent, it is the first component that is taken
in the case of vectors.
The directive EPDV makes sense only for a standalone system,
for example the fluid within a reservoir. In the remaining cases,
it is suggested to use EEXT, which gives the work of the
applied external forces.
Note:
In FE, the contribution of pressure work W_PDV
on the variation of kinetic energy is neglected in relation to the internal energy variation,
which is relevant for smooth solutions. In FV, W_PDV is computed as the variation of total energy,
which is always the work of pressure forces for a standalone domain.
The directive EINJ is only valid for material EAU.
14.6.6 Curve (Global Quantities)
ED.110
Object:
Definition of some global quantities to be drawn or listed, e.g.
relative to energy balance or spatial time step partitioning.
Syntax:
"COURBE" nuco < 'nomcourbe' >
[ "WINT" ;
"WEXT" ;
"WCIN" ;
"WTOT" ;
"WIMP" ;
"WSYS" ;
"BILAN" ;
"WSUM" <COMP icomp> ;
"DTMI" ;
"DTMA" ;
"MXSU" ;
"DT1" ;
"NSPL" ;
"NUSP" ;
"NSPT" ;
"NUSE" ;
"NACT" ;
"NUSN" ;
"LMAX" ;
"LMIN" ]

nuco


Identifier of the curve (reference for TRAC, XMGR, K2000
or LISTE).
A (unique) integer number, freely chosen by the user, by which the curve
may be successively referred to when needed.
 ’nomcourbe’


Name of the curve (reference for the user). This will appear on plots, etc.
 WINT


Internal energy.
 WEXT


External work.
 WCIN


Kinetic energy.
 WTOT


Sum of all external energies (see comments below).
 WIMP


Energy dissipated during contact/impact calculations.
 WSYS


Total energy of the system (see comments below).
 BILAN


Energy balance.
 WSUM


Sum of the auxiliary energy terms, see below (vector).
 DTMI


Minimum time increment in the time spatial step partitioning algorithm.
This quantity is available only in calculations with partitioning
(OPTI PART, see Page H.20).
 DTMA


Maximum time increment in the time spatial step partitioning algorithm.
This quantity is available only in calculations with partitioning
(OPTI PART, see Page H.20).
 MXSU


Logarithm in base 2 of the
maximum depth of the time spatial step partitioning algorithm.
This quantity is available only in calculations with partitioning
(OPTI PART, see Page H.20).
 DT1


Time integration step (scalar). This is the time increment that has led
to the current time. However, at the initial time of the calculation
(step 0, i.e. NPAS=0) this quantity does not make sense, so we
take DT2 instead, i.e. the time increment that will lead to the
following time.
 NSPL


Number of elements which have been split during the current time step.
 NUSP


Number of elements which have been unsplit during the current time step.
 NSPT


Total number of elements which have been split during the calculation.
 NUST


Total number of elements which have been unsplit during the calculation.
 NUSE


Number of used elements (active or inactive) at the current time step.
 NACT


Number of active elements at the current time step.
 NUSN


Number of used (and also of active) nodes at the current time step.
 LMAX


Maximum element level among all currently active elements
at the current time step.
 LMIN


Minimum element level among all currently active elements
at the current time step. Level 0 (unused
elements) is not considered in computing this quantity.
Also currently used but inactive elements are excluded.
 icomp


Index of the chosen component (only for vector quantities).
Comments:
The directive COUR can be repeated as many times as desired,
but each time with a different identifier.
Curve identifiers may be freely chosen by the
user, and the order in which they are given is irrelevant.
WTOT is the sum of all the “external” energies of the system:
the work of external forces, the injected energy, the energy due
to oil pyrolisis, etc.
WTOT is used in the calculation of the energy balance.
WIMP is the energy dissipated due to contactimpact phenomena.
This dissipation may come from the impact model used (soft impact,
hard impact) in conjunction with the temporal discretization of the problem.
WSYS is the energy of the system, defined as:
WSYS = WTOT + WIMP.
In a closed system, WSYS must be conserved.
As concerns the global auxiliary energy terms (WSUM),
the following components are available at the moment:

WSUM 1 ⇒ Energy dissipated by artificial viscosity (WARD)
 WSUM 2 ⇒ Pressure work for fluids −PdV (W_PDV)
 WSUM 3 ⇒ Energy injected or lost at the walls (W_INJ)
 WSUM 4 ⇒ Kinetic energy for CCFV Elements on X axis
 WSUM 5 ⇒ Kinetic energy for CCFV Elements on Y axis
 WSUM 6 ⇒ Kinetic energy for CCFV Elements on Z axis
 WSUM 7 ⇒ Total Energy for CCFV Elements
 WSUM 8 ⇒ Used for saving initial injected energy
 WSUM 9 ⇒ Total energy of the liquid phase (Only ADCR/ADCJ Model)
 WSUM 10 ⇒ Total energy of the bubble (Only ADCR/ADCJ Model)
 WSUM 11 ⇒ Total energy of the cover gas (Only ADCR/ADCJ Model)
 WSUM 12 ⇒ Kinetic energy of the liquid phase (Only ADCR/ADCJ Model)
 WSUM 13 ⇒ Kinetic energy of the bubble (Only ADCR/ADCJ Model)
 WSUM 14 ⇒ Kinetic energy of the cover gas (Only ADCR/ADCJ Model)
 WSUM 15 ⇒ Internal energy of the liquid phase (Only ADCR/ADCJ Model)
 WSUM 16 ⇒ Internal energy of the bubble (Only ADCR/ADCJ Model)
 WSUM 17 ⇒ Internal energy of the cover gas (Only ADCR/ADCJ Model)
Quantities 4 to 17 were added to account for auxiliary energies needed in FV cases.
Contrary to FE, Total and kinetic energy FV contributions have to be computed
at elements and not at nodes.
Quantities 9 to 17 are only relevant for the ADCR/ADCJ Model, it will return 0 in other cases.
Note:
All printed energy quantities are equivalent
in FE and FV cases, except forW_PDV : In FE, the contribution of pressure work W_PDV
on the variation of kinetic energy is neglected in relation to the internal energy variation,
which is relevant for smooth solutions. In FV, W_PDV is computed as the variation of total energy,
which is always the work of pressure forces for a standalone domain.
Note that the global quantities NSPL to LMIN in the above list
are available only in calculations with adaptivity
and with STAT option activated (OPTI ADAP STAT, see Page H.180).
14.6.7 Curve in space (Nodal Variables)
ED.112
Object:
Definition of the variables relative to nodes to be drawn or listed
as a function of space and not of time (as by default).
The space is here represented by a curvilinear abscissa, which is
built up starting by the definition of a sequence of nodes.
Syntax :
"SCOURBE" nuco < 'nomcourbe' >
$[ "T" t ; "NPAS" npas ; "NSTO" nsto ]$
"SAXE" scoe 'nom_saxe' <"INIT"> /LECTURE/
[ "COOR" ; "DEPL" ; "VITE" ; "ACCE" ; "FINT" ; "FEXT" ;
"FLIA" ; "ADFT" ; "MCPR" ; "MCRO" ; "MCTE" ; "MCMF" ;
"MCUX" ; "MCUY" ; "MCUZ" ; "SIGN" ; "ECRN" ; "LFNO" ;
"LFNV" ; "ILNO" ; "DTNO" ; "VITG" ; "MASN" ]
[ "COMP" icomp ; "NORME" ]

nuco


Identifier of the curve (reference for TRAC, XMGR, K2000
or LISTE).
A (unique) integer number, freely chosen by the user, by which the curve
may be successively referred to when needed.
 ’nomcourbe’


Name of the curve (reference for the user). This will appear on plots, etc.
 t


Time of the desired storage station from which results have
to be read in.
If option STEP IO is active, then the code looks for the
precise time t specified (within a small tolerance)
among all stored time stations and, if no such time is found,
an error message is issued.
If option STEP LIBR is active, the code takes the first
stored time station (if any) at a time equal to or greater than the
specified time. Again, if no such time is found then an error
message is issued.
 npas


Time step number of the desired storage station
from which results have to be read in.
 nsto


Storage index number of the desired storage station
from which results have to be read in.
 SAXE


Introduces the definition of the curvilinear abscissa to be used as
xaxis for the curve.
 scoe


Multiplicative coefficient for the values of the curvilinear abscissa
used as xaxis for the curve.
By default, the abscissa is built up according to the distance between
nodes, in the order they are defined in the following /LECTURE/.
 ’nom_saxe’


Name of the curvilinear abscissa. This will appear on plots, etc.
 INIT


Build up curvilinear abscissa by using the initial nodal
positions and not the current ones.
 /LECTURE/


List of nodes defining the curvilinear abscissa. They are taken in the
order given by the user (not reordered).
 COOR


Coordinate.
 DEPL


Displacement.
 VITE


Velocity.
 ACCE


Acceleration.
 FINT


Internal force.
 FEXT


Total external force.
 FLIA


External force due to liaisons (links).
 ADFT


Advectiondiffusion temperature.
 MCPR


Finite volume (MC) pressure.
 MCRO


Finite volume (MC) density.
 MCTE


Finite volume (MC) temperature.
 MCMF


Finite volume (MC) component mass fraction.
 MCUX


Finite volume (MC) fluid velocity along X computed
from the conserved variable (u_{x} = (ρ u_{x}) / ρ)).
 MCUY


Finite volume (MC) fluid velocity along Y computed
from the conserved variable (u_{y} = (ρ u_{y}) / ρ)).
 MCUZ


Finite volume (MC) fluid velocity along Z computed
from the conserved variable (u_{z} = (ρ u_{z}) / ρ)).
 SIGN


Spectral element stress.
 ECRN


Spectral element internal variable.
 LFNO


Logarithm in base 2 of the
level factor associated with a node
in the spatial time step partitioning algorithm.
 LFNV


Logarithm in base 2 of the
level factor associated with a node, including the neighbours
in the spatial time step partitioning algorithm.
 ILNO


Flag indicating whether a node is (1) or is not (0) subjected
to a link condition, used
in the spatial time step partitioning algorithm.
 DTNO


Stability time step associated with a node, used
in the spatial time step partitioning algorithm.
 VITG


Grid velocity (ALE only).
 MASN


Nodal mass.
 COMP


Introduces the chosen component.
 icomp


Component number.
 NORM


The norm of the considered vector (where applicable) is drawn.
Comments :
The directive SCOURBE can be repeated as many times as desired,
but each time with a different identifier. Identifiers should of
course also be different from those of curves defined by
the other curvedefinition directives (COURBE, RCOURBE,
DCOURBE).
Curve identifiers may be freely chosen by the
user, and the order in which they are given is irrelevant.
If neither T nor NPAS nor NSTO
are specified, then the last storage station is taken by default.
The keyword FORC is accepted as a synonym of FEXT
for backward compatibility, but
is obsolescent and should not be used in new input files.
14.6.8 Curve in space (Element Variables)
ED.113
Object:
Definition of the variables relative to elements to be drawn or listed
as a function of space and not of time (as by default).
The space is here represented by a curvilinear abscissa, which is
built up starting by the definition of a sequence of nodes.
Syntax :
"SCOURBE" nuco < 'nomcourbe' >
$[ "T" t ; "NPAS" npas ; "NSTO" nsto ]$
"SAXE" scoe 'nom_saxe' <"INIT"> /LECTURE/
< "SUPP" /LECT_ELEM/ >
[ "CONT" ; "ECRO" ; "EPST" ; "ENEL" ; "WAUX" ; "LFEL" ;
"LFEV" ; "DTEL" ; "CERR" ; "MAXC" ; "ERRI" ; "CLEN" ;
"ILEN" ; "MASE" ]
"COMP" icomp [ "GAUS" igaus ; "GAUZ" igauz ]
"VCVI" [ "COMP" icomp ; "NORM" ]

nuco


Identifier of the curve (reference for TRAC, XMGR, K2000
or LISTE).
A (unique) integer number, freely chosen by the user, by which the curve
may be successively referred to when needed.
 ’nomcourbe’


Name of the curve (reference for the user). This will appear on plots, etc.
 t


Time of the desired storage station from which results have
to be read in.
By default, the last storage station is taken.
 npas


Time step number of the desired storage station
from which results have to be read in.
By default, the last storage station is taken.
 nsto


Storage index number of the desired storage station
from which results have to be read in.
By default, the last storage station is taken.
 SAXE


Introduces the definition of the curvilinear abscissa to be used as
xaxis for the curve.
 scoe


Multiplicative coefficient for the values of the curvilinear abscissa
used as xaxis for the curve.
By default, the abscissa is built up according to the distance between
nodes, in the order they are defined in the following /LECTURE/.
 ’nom_saxe’


Name of the curvilinear abscissa. This will appear on plots, etc.
 INIT


Build up curvilinear abscissa by using the initial nodal
positions and not the current ones.
 /LECTURE/


List of nodes defining the curvilinear abscissa. They are taken in the
order given by the user (not reordered).
 SUPP /LECT_ELEM/


The optional keyword SUPP allows to specify, via the following
/LECT_ELEM/ directive, the geometrical support (list of the elements)
to be considered
for the projection onto nodes of the chosen element variable.
By default, all elements of continuum, shell or beam type present
in the mesh are considered. However, the default behaviour may lead to
wrong results, for example in the case of shells whose nodes are merged
with continuum fluid elements. If one traces, say, the pressure in the
fluid, then also the (unrelated) value in the shell would be considered
by default. To avoid the problem, specify SUPP LECT fluid TERM,
where fluid is an object containing only the fluid elements.
The SUPP directive should also be used in adaptivity
for the definition of space curves (SCOU) involving elemental quantities,
even in the absence of merged nodes. This allows to avoid ambiguities
in the formation of the curvilinear abscissa starting from the
base nodes, which are the only ones declared by the user.
 CONT


Stress tensor.
 ECRO


Hardening quantity.
 EPST


Total deformation tensor.
 ENEL


Internal energy.
 WAUX


Auxiliary energy terms for the element (see details below).
 LFEL


Logarithm in base 2 of the
level factor associated with an element in the spatial time step
partitioning algorithm.
 LFEV


Logarithm in base 2 of the
level factor associated with an element including its neighbours
in the spatial time step partitioning algorithm.
 DTEL


Stability time step Δ t_{stab} associated with the element.
The stability step is the critical
step Δ t_{crit} estimated by the code (roughly the element length
L divided by the speed of sound c in the element material)
multiplied by the safety coefficient φ (CSTA,
by default 0.8):
Δ t_{stab}=φΔ t_{crit}≈φL/c.
 CERR


Constant used in element error indicator calculation (adaptivity),
see the CERR input keyword of the ADAP directive on page B.210.
 MAXC


Maximum principal curvature of leastsquares fitting function,
used for element error indicator calculation (adaptivity).
 ERRI


Element error indicator (adaptivity).
 CLEN


Current characteristic element length
used in element error indicator calculation (adaptivity).
 ILEN


Optimal (indicated) characteristic element length
resulting from error indicator calculations (adaptivity).
 MASE


Element mass.
 VCVI


Material or particle velocity (first idim components) in Finite Volumes
Cell Centred model. Note that these vectors are not represented at the
nodes but at the “elements” (i.e. Finite Volumes) centroids.
 COMP


Introduces the component (unused for ENEL, LFEL, LFEV
and DTEL).
 icomp


Number of the component.
 GAUSS


Introduces the Gauss point (only for the quantities
CONT, EPST and ECRO).
 igau


Number of Gauss point chosen.
 GAUZ


Introduces the Gauss point through the thickness (only for the quantities
CONT, EPST and ECRO).
 igau


Number of Gauss point through the thickness.
 NORM


The norm of the VCVI vector is drawn.
Comments :
The directive SCOURBE can be repeated as many times as desired,
but each time with a different identifier. Identifiers should of
course also be different from those of curves defined by
the other curvedefinition directives (COURBE, RCOURBE,
DCOURBE).
Curve identifiers may be freely chosen by the
user, and the order in which they are given is irrelevant.
If the keyword GAUSS is omitted, the first integration
point is considered. If GAUSS is set to 0, the average
over all integration points is used.
As concerns the auxiliary energy terms for the element (WAUX),
the following components are avaliable at the moment:

WAUX 1 ⇒ Energy dissipated by artificial viscosity (WARD)
 WAUX 2 ⇒ Pressure work for fluids −PdV (W_PDV)
 WAUX 3 ⇒ Energy injected or lost at the walls (W_INJ)
 WAUX 4 ⇒ Kinetic energy for CCFV Elements on X axis
 WAUX 5 ⇒ Kinetic energy for CCFV Elements on Y axis
 WAUX 6 ⇒ Kinetic energy for CCFV Elements on Z axis
 WAUX 7 ⇒ Total Energy for CCFV Elements
 WAUX 8 ⇒ Used for saving initial injected energy
 WAUX 9 ⇒ Total energy of the liquid phase (Only ADCR/ADCJ Model)
 WAUX 10 ⇒ Total energy of the bubble (Only ADCR/ADCJ Model)
 WAUX 11 ⇒ Total energy of the cover gas (Only ADCR/ADCJ Model)
 WAUX 12 ⇒ Kinetic energy of the liquid phase (Only ADCR/ADCJ Model)
 WAUX 13 ⇒ Kinetic energy of the bubble (Only ADCR/ADCJ Model)
 WAUX 14 ⇒ Kinetic energy of the cover gas (Only ADCR/ADCJ Model)
 WAUX 15 ⇒ Internal energy of the liquid phase (Only ADCR/ADCJ Model)
 WAUX 16 ⇒ Internal energy of the bubble (Only ADCR/ADCJ Model)
 WAUX 17 ⇒ Internal energy of the cover gas (Only ADCR/ADCJ Model)
Quantities 4 to 17 were added to account for auxiliary energies needed in FV cases.
Contrary to FE, Total and kinetic energy FV contributions have to be computed
at elements and not at nodes.
Quantities 9 to 17 are only relevant for the ADCR/ADCJ Model, it will return 0 in other cases.
Note:
All printed energy quantities are equivalent
in FE and FV cases, except forW_PDV : In FE, the contribution of pressure work W_PDV
on the variation of kinetic energy is neglected in relation to the internal energy variation,
which is relevant for smooth solutions. In FV, W_PDV is computed as the variation of total energy,
which is always the work of pressure forces for a standalone domain.
14.6.9 Curve Read In from a File
ED.115
Object:
Definition of curves to be read in from a file.
The file must have been previously produced by EUROPLEXUS itself
by means of the SORT LIST command, and is a file of type “PUNCH”,
see page ED.125.
Syntax :
"RCOURBE" nuco 'nomcourbe' FICH 'nom_fic'
<"RENAME" 'new_name'> <"FACX" fx> <"FACY" fy>

nuco


Identifier of the curve (reference for TRAC, XMGR, K2000
or LISTE).
A (unique) integer number, freely chosen by the user, by which the curve
may be successively referred to when needed.
 ’nomcourbe’


Name of the curve (reference for the user). This will appear on plots, etc.
Unlike for the other curve definitions, this name is mandatory here
and must exactly match the name by which the curve has been
stored on the punch file during a previous EUROPLEXUS run.
 nom_fich


Name of the punch file enclosed in apostrophes.
 RENA


Allows to change the name of the curve if so desired.
 new_name


New name of the curve enclosed in apostrophes.
 FACX


Allows to change the xscale of the curve if so desired.
 fx


Multiplicative factor for the xvalues.
 FACY


Allows to change the yscale of the curve if so desired.
 fy


Multiplicative factor for the yvalues.
Comments :
The directive RCOURBE can be repeated as many times as desired,
but each time with a different identifier. Identifiers should of
course also be different from those of curves defined by
the other curvedefinition directives (COURBE, SCOURBE,
DCOURBE).
Curve identifiers may be freely chosen by the
user, and the order in which they are given is irrelevant.
This directive allows to retrieve curves from different calculations
and to compare them by plotting them on the same graph.
The time scales and the number of points
of the various curves are different in general. The
program automatically takes this into account.
Warning :
A certain care should be taken concerning the units of measurement
of curves stored and later retrieved for plotting. Note that curves
are stored with exactly the xvalues and the yvalues as they
would appear on a drawing. In particular, if the coefficients
AXTE coef, see page ED.60 and AXES coef, see page ED.125,
are not unitary, the stored values are multiplied by these
coefficients.
When the data are subsequently read in by RCOU, the scaling
is already included. So, plotting them by respecifying
again AXTE coef and/or AXES coef would probably
not have the desired effect, since the coefficients would be
applied twice! The results may be particularly confusing if the
curves read from file are plotted together with “normal”
curves (for which the coefficients are only applied once).
There is a simple way of avoiding this type of problem: when
defining curves to be stored on file for subsequent plottings or
comparisons, it is advisable to always specify AXTE 1.0
and AXES 1.0. In this way all curves are saved with their
“native” units of measurement. Any scale coefficients may be applied
later, during the actual plotting phase.
In case of need, it is possible to assign a new name to a readin
curve by means of the RENA directive. This is the name
that will appear on the plot legend. However, do not confuse
this with the original name of the curve (nomcourbe) which
must in any case exactly match the name stored in the file
in order to select the desired curve.
A mechanism for changing the scales of a readin curve both in
x and in y is offered by means of the FACX and FACY
directives. This is another way of overcoming the difficulties mentioned above
concerning the scale factors. However, their use should be
avoided whenever possible. The method outlined above of using
unit factors at storage is cleaner and much preferable.
Comments about the .pun file format:
In case that the pun file should be used for external data the following format
restrictions must be followed:

The file starts with the word "VALUES".
 The number of stored values is given between the character 7 and 12 of the first line.
 Characters 18:27 are the word COMPONENTS.
 Character 28 and 29 of the first line define the number of components.
 The next line consists from the name of the axe X (6:21) and axe Y (23:38).
 The next line contains the name of the curves (curve X 6:21 and curve Y 23:38).
The last part is important since that is the name of the curve
that must be defined in the RCOU command.
 After that, all values are defined by two fields of a length of 17 characters
(2E17.6). Each couple must be written in a separate line.
14.6.10 Curve Defined By The User
ED.118
Object:
Definition of curves in the form of tables containing a sequence
of (xy) values. These curves may represent a (piecewise)
analytical solution, or even an experimental result, to be compared
with numerical solutions by EUROPLEXUS.
The table containing the couples of values may be specified directly
within the present directive, or refer to a function previously
defined by the directive FONCTION, see page E.15, or represent
an analytical solution to a perfect gas shock tube problem.
The second possibility allows to plot and to visually check
the functions which are
defined and used in the calculation.
Syntax :
"DCOURBE" nuco < 'nomcourbe' >
[ npt*(x y) ;
"FONC" ifonc ;
"SHTU" "GAMM" gamm "ROM" rom "ROP" rop
"EINT" eint "LENM" lenm "LENP" lenp "TIME" time
"NRAR" nrar "VARI" vari ]

nuco


Identifier of the curve (reference for TRAC, XMGR, K2000
or LISTE).
A (unique) integer number, freely chosen by the user, by which the curve
may be successively referred to when needed.
 ’nomcourbe’


Name of the curve (reference for the user). This will appear on plots, etc.
 npt


Number of (xy) couples defining the curve (i.e. number of points).
In this case the values table is specified directly.
 x


Value of the abscissa.
 y


Corresponding value of the ordinate.
 ifonc


Index of a function previously defined by the directive FONCTION,
see page E.15.
 SHTU


Introduces the parameters of the perfect gas shock tube problem
for which the analytical solution (space curve of a chosen
variable along the tube length) has to be generated.
The highpressure zone is assumed to be in the left part of the
tube, of length lenm.
The lowpressure zone is assumed to be in the right part of the
tube, of length lenp.
The initial specific energy (and hence the initial temperature) is
the same in both parts. The initial density, and hence
the initial pressure, is higher in the left part than in the
right part of the tube.
 gamm


Ratio γ between the specific heat C_{p} at constant pressure
and the specific heat C_{v} at constant volume of the perfect gas.
 rom


Initial density ρ_{m} in the left part of the tube (highpressure zone).
 rop


Initial density ρ_{p} in the right part of the tube (lowpressure zone).
 eint


Initial specific energy i_{0} of the perfect gas.
 lenm


Length l_{m} of the left part of the tube (highpressure zone).
 lenp


Length l_{p} of the right part of the tube (lowpressure zone).
 time


Time t at which the analytical solution should be produced.
 nrar


Number of spatial intervals n_{r} at which the analytical
solution has to be computed in the rarefaction zone.
 vari


Desired output variable for the analytical solution:
1 means pressure, 2 means density, 3 means specific internal energy,
4 means sound speed, 5 means velocity.
Comments :
The directive DCOURBE can be repeated as many times as desired,
but each time with a different identifier. Identifiers should of
course also be different from those of curves defined by
the other curvedefinition directives (COURBE, SCOURBE,
RCOURBE).
Curve identifiers may be freely chosen by the
user, and the order in which they are given is irrelevant.
This directive allows to define arbitrary curves
and to compare them with curves built up from EUROPLEXUS
results by plotting them on the same graph.
The time scales (or more generally the abscissas) and the number of points
of the various curves are different in general. The
program automatically takes this into account.
If a curve is specified by means of a function previously defined
by the directive FONCTION, then:

If the function is of type TABL, then the (xy) values
of the table function are directly used for the curve.
 If the function is of type ROUT (see user routine TABANA)
or of type LSQU (leastsquares fitting), then the xvalues are
not specified in the function. The code will try to use the stored time values
for the current calculation as the xvalues and to compute the corresponding
yvalues by calling the specified function.
 Other types of functions are not accepted at the moment and
an error message is issued.
14.6.11 Set of PochhammerChree curves
ED.119
Object:
Automatic generation of a set of curves
for PochhammerChree equation verification.
The user must have previously read in results from a .POC file
by means of the RESU directive, in addition to reading (global) results
from an ordinary results file (typically an ALICE file).
Syntax :
"PCOURBE" "YOUN" youn "NU" nu "RHO" rho "R" r
"NM" nm "IDOF" idof
<"DHAR" dhar "TOL" tol "STEP" step "N1" n1 "AXTE" axte "FREQ" freq "M" m>

youn


Young’s modulus of the bar material.
 nu


Poisson’s coefficient of the bar material.
 rho


Density of the bar material.
 r


Radius of the cylindrical bar.
 nm


Number of the dispersive modes that will be calculated.
 idof


Global dof along which the chosen variable is considered:
1 means radial direction, 2 means axial direction. A
2D axisymmetric calculation (with the bar axis directed
vertically along the yaxis) is assumed.
 dhar


Number of harmonics (or frequencies) that participate in the solution. In the case of the single harmonic excitation
it should be 1.
By default, 250 harmonics are taken.
 tol


Relative error between an analytical and numerical solution.
By default, it is 0.05.
 step


Number of increments that will be used in the area of the relative error
in order to identify a solution.
By default, it is 200.
 n1


Identifier (number) of the first generated curve.
By default, it is 1.
 axte


The name of the xaxis that will be used in the plotting of the curves.
By default, it is ’RAD/WAVELENGTH’.
 freq


The frequency of the excitation load (used only for the case of the single harmonic load).
 m


The m ratio between the thickness of the shell and the mean radius of the hollow cylinder (in the case of hollow cylinder).
By default, it is 0.
Comments :
The directive PCOURBE automatically generates three sets
of curves. The first set (ranging from n1 to
n1 + nm  1) contains the analytical solutions, one for
each chosen mode. These curves have the following names:
Mode_1, Mode_2 etc.
The second set (ranging from n1 + nm to
n1 + 2*nm  1) contains the numerical solutions, one for
each chosen mode. These curves have the following names:
Nume_1, Nume_2 etc. The third set (ranging from n1 + 2*nm to
n1 + 2*nm + nlines*dhar  1) contains the wavenumber spectrum for all the frequencies of
interest for all the lines (parallel to the axis of the rod) of the calculation. The peaks on the wavenumber spectrum indicates
the specific mode wavenumber for each frequency. These curves have the following name:
LINE_1, LINE_2 etc.
Note that any preexisting curves with the same identifiers will be erased.
The phenomenon of dispersion is the reason why waves with different wavelengths will travel
at different speed in the same material. The new module is dealing with the propagation of compressional
waves in isotropic cylinders. It calculates the dispersion curves corresponding to each mode of propagation.
The dispersion curves for each mode of propagation show the relationship between the phase velocity and the
wavelength of a specific material. The procedure of defining those curves is described below in 7 steps

An axial step function load is imposed in the circular face of the bar.
 Velocity versus time data are calculated and stored at equally spaced points along a
predefined line in the axial direction of the bar.
 An FFT analysis is performed for each set of these time data in order to obtain the frequency
spectrum for each point. This spectrum data are calculated and stored in order to be used in the next step.
 For each frequency, a history in the space domain across the predefined line is calculated and stored.
This history can be calculated if the value of spectrum data is used for every point of the line for the desired frequency.
 By performing an FFT analysis on the space domain history across the predefined line,
a wavenumber spectrum can be obtained for each frequency. These results corresponds to the third set of curves
produced under PCOURBE directive.
 Each peak of the wavenumber spectrum corresponds to specific mode wavenumber for each frequency.
The identification of the peaks for each frequency, leads to one point on the dispersion curves for
each mode (for the modes that appeared in the desired frequency). Each peak indicates a wave number for
the desired frequency and from this pair of values (wavenumber and frequency) the phase velocity and the
wavelength of the mode can be defined. Lower modes peaks are located in higher wavenumbers.
 Finally the numerical results are compared with the analytical results of PochhammerCree solution.
In the case where the m directive is defined, the hollow cylinder case is considered for the
calculation of the analytical solution.
The MirksyHerrman frequency equation is used in the case of the hollow cylinder. Also the user
is encouraged to use the hole directive in
order to define the inner radius of the hollow cylinder.
14.6.12 Drawings (TRACE)
ED.120
Object:
This instruction is aimed at defining the drawings to be produced.
Syntax:
"TRACE" ( nuco ) $["PS" ; <"TEXT"> ; "MIF" ]$
"AXES" coef 'nom_axe_Oy'
<"XAXE" nxax coex 'nom_axe_Ox'>
<"COLO" (co)>
<"THIC" (th)>
<"DASH" (da)>
< $[ "NOLI" ; "LINE" (li) ]$ >
<"SYMB" <(sy)>> <"SYSC" sysc>
<"NOXL" (nx)>
<"NOYL" (ny)>
<"XZER"> <"YZER">
<"XGRD"> <"YGRD">
<"XLOG"> <"YLOG">
<"XMIN" xmin "XMAX" xmax $[ "DX" dx ; "NX" nx ]$>
<"YMIN" ymin "YMAX" ymax $[ "DY" dy ; "NY" ny ]$>

nuco


Identifiers of the curves to be drawn (at most 12 curves).
 PS


Draw on a PostScript file (this is the default).
 TEXT


In addition to drawing on a PostScript file, also produce a
list of the drawn data in tabular form (xvalue, yvalue)
on a text file. The name of this file is
<base>.txt, where <base> is the base name of the
current calculation.
 MIF


Draw on a MIF file. MIF is Adobe FrameMaker’s language and may be
suited to embed the graphics in a FrameMaker document. The drawing
remains fully editable in FrameMaker (line style, colors, fonts etc.).
 coef


Multiplying coefficient to change the units of the Oy axis.
 ’nom_axe_Oy’


Name of the Oy axis (at most 16 characters).
 nxax


Optional identifier of a curve to be used for the xaxis.
By default, the drawing of the specified curves is done vs. time.
However, by specifying the XAXE subdirective, it is possible to produce
a combined graph in which one or more quantities are plotted vs.
another quantity rather than vs. time. For example, a σє
graph may be produced.
 coex


Multiplying coefficient to change the units of the Ox axis.
 ’nom_axe_Ox’


Name of the Ox axis (at most 16 characters).
 COLO


Optional keyword that introduces the colors to be used for the
various curves. If omitted, all curves are drawn in black.
 co


Name of the color for the curve, (not enclosed in quotes).
This must be repeated exactly as many
times as there are curves in the drawing (see nuco above).
The valid names are those
of Cast3m, i.e. bleu, roug, rose, vert,
turq, jaun, blan or noir.
 THIC


Optional keyword that introduces the line thicknesses to be used for the
various curves, in points. If omitted, all curves are drawn
with a line thickness of 0.1 points.
 th


Line thickness for the curve, in points. This must be repeated exactly as many
times as there are curves in the drawing (see nuco above).
 DASH


Optional keyword that introduces the dash patterns to be used for the
various curves. If omitted, all curves are drawn
as solid lines.
 da


Code for the curve dash pattern. This must be repeated exactly as many
times as there are curves in the drawing (see nuco above).
Valid dash pattern codes are: 0 for a solid line, 1 for
long dashes, 2 for medium dashes, 3 for short dashes, 4 for extrashort
dashes, and 5 for longshort dashes.
 NOLI


Do not draw any lines connecting points on (all) the curves.
 LINE


Choose which curve(s) should be drawn as lines or not.
 li


Code for the line connecting the curve points.
This must be repeated exactly as many
times as there are curves in the drawing (see nuco above).
Valid line codes are: 0 means no line, 1 means line
(with the chosen color, thickness and dash pattern, if any).
 SYMB


Draw a symbol at each data point on each of the curves. The symbol is drawn
in addition to the curve line. To remove the line (leaving only the
symbols), use the NOLI or the LINE (li) keywords described above.
To selectively choose which curves will get symbols, and/or the symbol used
for each curve, specify the following (optional) sequence (sy).
By default (no (sy) specified), symbol types 1 to 12 (see below)
are used for curves 1 to 12.
 sy


Code for the symbol drawn on each curve data point.
If present, this must be repeated exactly as many
times as there are curves in the drawing (see nuco above).
Symbols are drawn with the same color and thickness as the associated curve.
Valid symbol codes are: 0 no symbol, 1 plus, 2 cross, 3 square,
4 octagon, 5 triangle north, 6 triangle south, 7 triangle east,
8 triangle west, 9 hourglass, 10 hourglass horizontal, 11 diamond,
12 Y, 13 Z.
 SYSC


Introduce a symbol scaling factor sysc. By default, the factor is 1.0.
 NOXL


Optional keyword that introduces the definition of whether or not
the various curves participate in the definition of the xaxis
(automatic search of the limits and of the major and minor subdivisions).
If omitted, all curves participate in the definition of the xaxis.
 nx


Code for the curve participation in the definition of the xaxis.
This must be repeated exactly as many
times as there are curves in the drawing (see nuco above).
Valid codes are: 0 means that the curve participates in the definition
of the axis, 1 means that the curve is ignored in definition of the
axis.
 NOYL


Optional keyword that introduces the definition of whether or not
the various curves participate in the definition of the yaxis
(automatic search of the limits and of the major and minor subdivisions).
If omitted, all curves participate in the definition of the yaxis.
 ny


Code for the curve participation in the definition of the yaxis.
This must be repeated exactly as many
times as there are curves in the drawing (see nuco above).
Valid codes are: 0 means that the curve participates in the definition
of the axis, 1 means that the curve is ignored in definition of the
axis.
 XZER


Draw a vertical dotted line in correspondence of the abscissa x=0.
 YZER


Draw a horizontal dotted line in correspondence of the ordinate y=0.
 XGRD


Draw vertical grid lines at every major axis tick.
 YGRD


Draw horizontal grid lines at every major axis tick.
 XLOG


Use a logarithmic (10base) scale for the xaxis instead of a linear scale.
Obviously, all xvalues must be strictly positive.
 YLOG


Use a logarithmic (10base) scale for the yaxis instead of a linear scale.
Obviously, all yvalues must be strictly positive.
 XMIN


Use the specified lower limit for the xaxis instead of computing it
automatically.
 XMAX


Use the specified upper limit for the xaxis instead of computing it
automatically.
 DX


Use the specified scale increment for the xaxis instead of computing it
automatically.
 NX


Use the specified number of increments for the xaxis instead of computing it
automatically.
 YMIN


Use the specified lower limit for the yaxis instead of computing it
automatically.
 YMAX


Use the specified upper limit for the yaxis instead of computing it
automatically.
 DY


Use the specified scale increment for the yaxis instead of computing it
automatically.
 NY


Use the specified number of increments for the yaxis instead of computing it
automatically.
Comments:
The instruction TRAC may be repeated as many times as desired.
It is possible to use the same curve (same identifier) for several
drawings.
Normally the axes scales are computed automatically. However, the user may
take full control of this process by specifying XMAX ... and / or
YMAX .... When specifying a lower bound also the corresponding
upper bound and either the increment or the number of increments must
be specified as well.
Examples:
"TRAC" 1 4 2 "AXES" 1. 'PRESSION (PA) '
"TRAC" 1 2 "AXES" 1E6 'PRESSION (MPA)'
"TRAC" 6 "AXES" 1E6 'STRESS (MPA)' "XAXE" 5 1.0 'STRAIN'
14.6.13 Output on file (XMGR)
ED.121
Object:
Definition of the variables to be printed on the
auxiliary files directly readable by the XMGR software
(Copyright Paul J. Turner). See also the directive PERK on page
ED.60, which allows to change the default name of the output file.
Syntax:
"XMGR" ( nuco ) "AXES" coef 'nom_axe_Oy'
<"XAXE" nxax coex 'nom_axe_Ox'>

nuco


Identifiers of the curves to be printed (at most 12 curves).
 coef


Multiplying coefficient to change the units of the Oy axis.
 ’nom_axe_Oy’


Name of the Oy axis (at most 16 characters).
 nxax


Optional identifier of a curve to be used for the xaxis.
By default, the drawing of the specified curves is done vs. time.
However, by specifying the XAXE subdirective, it is possible to produce
a combined graph in which one or more quantities are plotted vs.
another quantity rather than vs. time. For example, a σє
graph may be produced.
 coex


Multiplying coefficient to change the units of the Ox axis.
 ’nom_axe_Ox’


Name of the Ox axis (at most 16 characters).
Comments:
The XMGR directive may be repeated as many times as needed.
The use of this directive is identical to that of directive TRACE.
It is possible to combine them by using the same curves:
Example:
"TRACE" 1 4 2 "AXES" 1. 'PRESSION (Pa)'
"XMGR" 4 2 "AXES" 1. 'PRESSION (Pa)'
The files created for XMGR have names of the form:
<base_xxx>.MGR, where <base> is the base name of
the current calculation and xxx is a counter.
A separate file is produced for each XMGR directive.
If no base name is available, then the file name becomes
TRACXMGR_xxx.MGR.
It is possible to use the same curve (same identifier)
for more than one list.
Examples:
"XMGR" 1 4 2 "AXES" 1. 'PRESSION (Pa)'
"XMGR" 1 2 "AXES" 1E6 'PRESSION (MPa)'
"XMGR" 6 "AXES" 1E6 'STRESS (MPA)' "XAXE" 5 1.0 'STRAIN'
14.6.14 Output on file (K2000)
ED.122
Object:
Definition of the variables to be printed on an
auxiliary file directly readable by the CASTEM 2000 software.
See also the directive PERF on page
ED.60, which allows to change the default name of the output file.
Syntax:
"K2000" ( nuco ) "AXES" coef 'nom_axe_Oy'
<"XAXE" nxax coex 'nom_axe_Ox'>

nuco


Identifiers of the curves to be printed (at most 12 curves).
 coef


Multiplying coefficient to change the units of the Oy axis.
 ’nom_axe_Oy’


Name of the Oy axis (at most 16 characters).
 nxax


Optional identifier of a curve to be used for the xaxis.
By default, the drawing of the specified curves is done vs. time.
However, by specifying the XAXE subdirective, it is possible to produce
a combined graph in which one or more quantities are plotted vs.
another quantity rather than vs. time. For example, a σє
graph may be produced.
 coex


Multiplying coefficient to change the units of the Ox axis.
 ’nom_axe_Ox’


Name of the Ox axis (at most 16 characters).
Comments:
The K2000 directive may be repeated as many times as needed.
The use of this directive is identical to that of directive TRACE.
It is possible to combine them by using the same curves:
Example:
"TRACE" 1 4 2 "AXES" 1. 'PRESSION (Pa)'
"K2000" 4 2 "AXES" 1. 'PRESSION (Pa)'
The formatted file may be directly inserted in the input data
for CASTEM 2000. The contained objects are of type "LISTREEL"
,
and the names are "L_TEMPS"
for the time and "L_number"
for the curves (number is the curve identifier).
It is possible to use the same curve (same identifier)
for more than one list.
Examples:
"K2000" 1 4 2 "AXES" 1. 'PRESSION (Pa)'
"K2000" 1 2 "AXES" 1E6 'PRESSION (MPa)'
"K2000" 6 "AXES" 1E6 'STRESS (MPA)' "XAXE" 5 1.0 'STRAIN'
14.6.15 Output on file (LIST)
ED.125
Object:
Definition of the variables to be printed on an
auxiliary file of type “PUNCH” (see also the
directive PERF).
Syntax:
"LISTE" ( nuco ) "AXES" coef 'nom_axe_Oy'
<"XAXE" nxax coex 'nom_axe_Ox'>

nuco


Identifiers of the curves to be printed (at most 12 curves).
 coef


Multiplying coefficient to change the units of the Oy axis.
 ’nom_axe_Oy’


Name of the Oy axis (at most 16 characters).
 nxax


Optional identifier of a curve to be used for the xaxis.
By default, the drawing of the specified curves is done vs. time.
However, by specifying the XAXE subdirective, it is possible to produce
a combined graph in which one or more quantities are plotted vs.
another quantity rather than vs. time. For example, a σє
graph may be produced.
 coex


Multiplying coefficient to change the units of the Ox axis.
 ’nom_axe_Ox’


Name of the Ox axis (at most 16 characters).
Comments:
The LISTE directive may be repeated as many times as needed.
The use of this directive is identical to that of directive TRACE.
It is possible to combine them by using the same curves:
Example:
"TRACE" 1 4 2 "AXES" 1. 'PRESSION (Pa)'
"LISTE" 4 2 "AXES" 1. 'PRESSION (Pa)'
The tables come out as nbco blocks of NT lines
with two numbers (xy values) each each
The first value is the abscissa (by default the time),
and the second value is the corresponding ordinate (yvalue).
Each block therefore fully describes one curve.
Blocks are given in the same order as they appear in directive LISTE.
To facilitate the subsequent reading of these tables,
each block is proceeded by three description lines:

On the first line, after the word VALEURS there is NT,
the number of lines of the block, that is also the number of xy couples.
Then comes the word COMPOSANTES, followed by the number
of yvalue columns (this number is always 1).
 On the second line, which starts by *, are given the names
of the Ox axis and of the Oy axis (string nom_axe_Oy
of directive AXES).
 On the third line, which also starts by *, are given the names
of the curves (nomcourbe) defined in COURBE.
It is possible to use the same curve (same identifier)
for more than one list.
Examples:
"LISTE" 1 4 2 "AXES" 1. 'PRESSION (Pa)'
"LISTE" 1 2 "AXES" 1E6 'PRESSION (MPa)'
"LISTE" 6 "AXES" 1E6 'STRESS (MPA)' "XAXE" 5 1.0 'STRAIN'
A certain care should be taken concerning the units of measurement
of curves stored and later retrieved for plotting. Note that curves
are stored with exactly the xvalues and the yvalues as they
would appear on a drawing. In particular, if the coefficients
AXTE coef, see page ED.60 and AXES coef, see above,
are not unitary, the stored values are multiplied by these
coefficients.
When the data are subsequently read in by RCOU, the scaling
is already included. So, plotting them by respecifying
again AXTE coef and/or AXES coef would probably
not have the desired effect, since the coefficients would be
applied twice! The results may be particularly confusing if the
curves read from file are plotted together with “normal”
curves (for which the coefficients are only applied once).
There is a simple way of avoiding this type of problem: when
defining curves to be stored on file for subsequent plottings or
comparisons, it is advisable to always specify AXTE 1.0
and AXES 1.0. In this way all curves are saved with their
“native” units of measurement. Any scale coefficients may be applied
later, during the actual plotting phase.
14.6.16 Find value on a curve (FVAL)
ED.126
Object:
Find values (abscissas) x of a curve for which the curve assumes
a given value v, i.e. for which y(x)=v.
Linear interpolation is used.
All found values of x are printed on the listing.
If y(x_{n})≤ v≤ y(x_{n+1}), or y(x_{n})≥ v≥ y(x_{n+1}),
then the value of x in the interval from x_{n} to x_{n+1} is
interpolated linearly by the expression:
x=x_{n}+  ⎛
⎝  x_{n+1}−x_{n}  ⎞
⎠  
(54) 
Syntax:
"FVAL" nuco val

nuco


Identifier of the curves to be examined.
 val


Value to be sought on the curve.
Comments:
Note that, like in the case of minimum and maximum values (MINM)
of curves, the found values (if any) are printed on the listing only when
the corresponding curve is drawn via the TRAC command.
Therefore, in order to get the desired values actually printed
make sure to first use the FVAL directive for the desired
curve(s) and then let the curve number appear in at least one
TRAC directive.
For example:
SORT GRAP ...
. . .
COUR 1 ...
COUR 3 ...
COUR 23 ...
. . .
FVAL 1 3.14 ! search value 3.14 on curve #1
FVAL 23 1.0 ! search value 1.0 on curce #23
. . .
TRAC 23 ...
FIN
In the above example, the value search for −1.0 in curve 23
is printed on the listing, but the search for value 3.14 in
curve 1 is not printed.
14.7 VISUALIZATIONS
ED.140
Object:
To produce, by reading results stored in the results file,
(a subset of) the visualizations that are possible
during direct execution of the code (see Pages A.25 and O.10).
These include graphical rendering interactively in a window or
in batch mode on file and
production of animations.
Not all visualization types and features are available, though (see
below for details).
Syntax:
( "VISU" $ "T" t ; "NPAS" npas ; "NSTO" nsto $
<PLAY>
<sequel of interactive commands, see pages A.25 and O.10>
<ENDPLAY>
)

t


Time of the desired (initial) storage station from which results have
to be read in.
Subsequent time stations may then be reached by suitable
commands (e.g. GO and FREQ)
in the PLAY ... ENDPLAY sequence.
 npas


Time step number of the desired (initial) storage station
from which results have to be read in.
Subsequent time stations may then be reached by suitable
commands (e.g. GO and FREQ)
in the PLAY ... ENDPLAY sequence.
 nsto


Storage index number of the desired (initial) storage station
from which results have to be read in.
Subsequent time stations may then be reached by suitable
commands (e.g. GO and FREQ)
in the PLAY ... ENDPLAY sequence.
 PLAY


Introduces a sequel of “interactive” commands (see pages A.25 and O.10) that
are read subsequently from the input file rather than from the keyboard.
 ENDP


Terminates the sequel of “interactive” commands (see pages A.25 and O.10) that
are read subsequently from the input file rather than from the keyboard.
Comments:
As indicated by the parentheses in the above syntax, the VISU
subdirective may be repeated as many times
as needed within the SORT directive (see Page ED.40).
However, only one SORT directive is allowed within
each input data set.
Repetition of the VISU subdirective (without repeating SORT)
may be useful e.g. to step back in the ALICE file, i.e. to
go to a previously saved time step. To step forth in the
ALICE file, simply use the GO and FREQ commands
in the PLAY ... ENDPLAY sequence, as mentioned above.
The options T, NPAS and NSTO
are mutually exclusive. Exactly one of them must be
specified, in order to position the
read cursor of the storage file at the initial storage
position of interest. Following storage positions may
then be accessed by the “interactive” commands if so desired
(e.g. to produce an animation).
Socalled “interactive” commands such as TRAC may then
be issued from the keyboard. Alternatively, they may be embedded
in the input file by enclosing them in the pair of keywords
PLAY ... ENDPLAY.
The read cursor may be advanced by means of the GO
command. In this case, however, the frequency FREQ
counts the storage stations rather than the time steps.
To terminate the execution of interactive commands (when typing
them actually at the keyboard) and
to return control to the input file, use the ENDP command.
Warnings:
Note that not all the visualization features described in pages A.25 and O.10
for direct execution of the code are available when visualizing
results from a results file. Most restrictions come from the
fact that the results file (typically an ALICE file) does not contain
all the information that is available during direct execution.
For example, the following features will not work:

Visualization of thicknesses.
 Visualization of materialrelated data.
 Etc. etc.
Note also that, although the RESU directive allows to
read data from several types of results files, not all of
them are suitable for visualizations. For example, an ALIC TEMP
results file typically contains only very limited information
(just a few nodes and elements) and therefore it is suitable
for the productiuon of graphs (time curves) but not of visualizations
involving the whole mesh.