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Code_Aster
®
Version
6.4
Titrate:
Use of the indicators of error and strategies of adaptation
Date
:
17/10/03
Author (S):
P. BADEL, O. BOITEAU, V. CANO
Key
:
U2.08.01-A
Page
:
1/30
Instruction manual
U2.08 booklet: Advanced function and control of calculations
HT-66/03/002/A
Organization (S):
EDF-R & D/AMA, SINETICS















Instruction manual
U2.08 booklet: Advanced functions and control of calculations
Document: U2.08.01



Use of the indicators of error and strategies
of adaptation of mesh associated




Summary:

This document describes the use in Code_Aster of the indicators of error and their use in a context
of adaptation of mesh. In this direction, it aims at making a synthesis intended to provide to the user the answers
preconditions to the use of the adaptation of mesh: where to find information in documentation
Is Code_Aster, which the perimeter of use, which are the good practices to be implemented?
Examples of use come to illustrate the possibilities and the implementation of strategies of mending of meshes.
background image
Code_Aster
®
Version
6.4
Titrate:
Use of the indicators of error and strategies of adaptation
Date
:
17/10/03
Author (S):
P. BADEL, O. BOITEAU, V. CANO
Key
:
U2.08.01-A
Page
:
2/30
Instruction manual
U2.08 booklet: Advanced function and control of calculations
HT-66/03/002/A
1 Introduction
The indicators of error and the adaptation of mesh are useful for the user to provide calculations them
more reliable possible with respect to the errors of discretization (due to the method finite elements
employee).
The indicators of error are calculated in postprocessing of Aster, while the adaptation of mesh
is carried out by call to an external program, specialized in this task,
LOBSTER
.
The goal of this document is to provide possible “point entrance” a most complete bound for
the user wishing to implement this kind of techniques in its calculations. The plan of the document
is then the following:
1) the perimeter of use (which can one make?) ;
2) references useful to read before use (where to go to seek information more
deepened that those brought in this document?) ;
3) a diagrammatic recall of the methodology of adaptation of mesh;
4) a recall of the controls and options to be used (how to write the command file?) ;
5) a whole of consultings on the “good practices” to implement (which are them
points worthy of attention during the use?) ;
6) some examples illustrating use of these techniques and consultings the given
previously (how to make in practice?).


2 Perimeter
of use
The field of application of the indicators of error and the adaptation of mesh is delimited by
following stresses (one will refer to the reference documents given below for more
details):
·
the errors taken into account are the errors of space discretization (thus the size of
elements employed); in particular, errors of discretization temporal (or pseudo
temporal in the case of non-linear materials) are apart from this perimeter;
·
the physical phenomena are limited to mechanics (linear or not-linear,
Cf below) and with thermics (idem.);
·
in mechanics as in thermics, the behavior can be linear or not linear (except
for the estimator of error of Zhu-Zienkiewicz in mechanics which treats only the behavior
linear), knowing that the theoretical results of the indicators of error are obtained in
linear field (their use in the non-linear field is thus not based on
theoretical results but on an empirical observation of their interest);
·
the elements used can be unspecified for the use of the indicators of errors (except
for the estimator of error of Zhu-Zienkiewicz in mechanics, which treats only the elements
2D; estimator ZZ2 does not accept that mesh made up either of triangles or of
quadrangles); on the other hand, the use of the adaptation of mesh with
LOBSTER
require
for the moment use of elements in the list (not, segment, triangle, tetrahedron) with exclusion
of very other. These elements can be linear or quadratic.
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Code_Aster
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Version
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Titrate:
Use of the indicators of error and strategies of adaptation
Date
:
17/10/03
Author (S):
P. BADEL, O. BOITEAU, V. CANO
Key
:
U2.08.01-A
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:
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3 References
useful
The documents [bib1] with [bib5] estimators of error and tool for adaptation of mesh treat
LOBSTER
.
The documents [bib6] with [bib8] form the support of the Aster formations on the subject.
Concerning the choice of the finite elements, one will be able to refer to the document [bib9].

[1]
X. DESROCHES: “Estimator of error of Zhu-Zienkiewicz in elasticity 2D”. [R4.10.01],
1994.
[2]
X. DESROCHES: “Estimator of error in residue”. [R4.10.02], 2000.
[3]
O. BOITEAU: “Indicating of space error in residue for transitory thermics”.
[R4.10.03], 2001.
[4]
G. NICOLAS & Al http://www.code_aster.org/outils/homard
[5]
G. NICOLAS: “Macro-control
MACR_ADAP_MAIL
”. Doc. [U7.03.01].
[6]
O. BOITEAU: Case-test. “Mechanical FORMA04 ­ adaptive Maillage on a beam in
bending “. Doc. [V6.03.119]
[7]
O. BOITEAU: Case-test. “FORMA05 ­ thermomechanical adaptive Maillage on a cylinder head
fissured “. Doc. [V6.03.120]
[8]
O. BOITEAU: Run and Indicating TP “of error and adaptation of mesh. State of the art and
establishment in Code_Aster “. http://www.code_aster.org/utilisation/formations
[9]
S. MICHEL-PONNELLE
: “
Note of use on the choice of the finite elements
”.
Doc. [U2.01.10]
General principle
The indicators of error used in Aster are indicators a posteriori, one gives one below
diagram specifying their use. One will find in the case-tests [bib6] and [bib7] like in the continuation
this document of the examples of use of the functionalities of the process control language Aster (based
on Python) adapted to this use.
1) Definition of the data of calculation (in
private individual mesh)
2) Resolution of the problem
3) Calculation of the indicators of error (post-
processing)
1) Definition of the data of calculation (in
private individual initial mesh)
2) Resolution of the problem
3) Calculation of the indicators of error (post-
processing)
4) Adaptation of the mesh (based on one of
indicators calculated at stage 3)
Use of the indicators of error
Use of the adaptation of mesh
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Code_Aster
®
Version
6.4
Titrate:
Use of the indicators of error and strategies of adaptation
Date
:
17/10/03
Author (S):
P. BADEL, O. BOITEAU, V. CANO
Key
:
U2.08.01-A
Page
:
4/30
Instruction manual
U2.08 booklet: Advanced function and control of calculations
HT-66/03/002/A
4
Recall of the controls and options Aster to be used
4.1
Estimator of error in mechanics of Zhu-Zienkiewicz
The calculation of the estimator of error is carried out directly in the operator
CALC_ELEM
with
options:
OPTION= `ERRE_ELEM_NOZ1'
for estimator ZZ1;
OPTION= `ERRE_ELEM_NOZ2'
for estimator ZZ2.
The calculation of the field (with the nodes) of smoothed stresses can separately be started (not very useful in
practical):
OPTION= `SIGM_NOZ1_ELGA'
for smoothing ZZ1
OPTION= `SIGM_NOZ2_ELGA'
for smoothing ZZ2
The estimator provides:
·
a field by element comprising 3 components:
“ERREST”
: the absolute error estimated on the element
()
K
;
“NUEST”
: the relative error estimated on the element
()
()
()
2
,
0
2
100
K
H
rel
K
K
K
+
×
=
;
“SIGCAL”
: the standard of energy of the calculated solution
K
H
,
0
;
·
exit-listing comprising same information at the total level.

4.2
Estimator of error in mechanics of the residue type
For calculating the indicator of error, it is necessary to carry out the calculation of the field (with the nodes by elements) of
stresses to normalize the error, by the operator
CALC_ELEM
:
OPTION= `SIGM_ELNO_DEPL'
in elasticity (afterwards
MECA_STATIQUE
);
OPTION= `SIEF_ELNO_ELGA'
into non-linear (afterwards
STAT_NON_LINE
).
The calculation of the estimator of error itself is also carried out in the operator
CALC_ELEM
with the options:
OPTION= `ERRE_ELGA_NORE'
for calculation at the points of Gauss;
OPTION= `ERRE_ELNO_ELGA'
for calculation with the nodes by elements.
The estimator provides:
·
a field by element comprising 3 components:
“ERREST”
: the absolute error estimated on the element
()
K
;
“NUEST”
: the relative error estimated on the element
()
()
()
2
,
0
2
100
K
H
rel
K
K
K
+
×
=
;
“SIGCAL”
: the standard of energy of the calculated solution
K
H
,
0
.
·
exit-listing comprising same information at the total level.
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Code_Aster
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Version
6.4
Titrate:
Use of the indicators of error and strategies of adaptation
Date
:
17/10/03
Author (S):
P. BADEL, O. BOITEAU, V. CANO
Key
:
U2.08.01-A
Page
:
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4.3
Estimator of error in thermics (of residues type)
The calculation of the estimator of error is carried out in the operator
CALC_ELEM
with the options:
OPTION= `ERTH_ELEM_TEMP'
for calculation by elements;
OPTION= `ERTH_ELNO_TEMP'
for calculation by elements with the nodes.
The estimator provides the following components (one will notice that all the fields are accessible
individually, one will underline the interest in the examples of it):
Absolute error
Relative error
Term of standardization

Term
voluminal
()
K
N flight
R 1
,
+
()
()
.
100
1
,
1
,
×
+
+
K
NR
K
N flight
R
N flight
R
()
K
N H
K
N flight
R
S
H
K
NR
,
0
1
,
1
,
:
+
+
=

TERMVO
TERMV2
TERMV1

Term of jump
()
K
N jump
R 1
,
+
()
()
.
100
1
,
1
,
×
+
+
K
NR
K
N jump
R
N jump
R
()
()
F
K
nh
F
N jump
R
F
K
N
T
H
K
NR
,
0
1
,
2
1
1
,
2
1
2
:
+
+
=
TERMSA
TERMS2
TERMS1

Term of flow
()
K
N flow
R 1
,
+
()
()
.
100
1
,
1
,
×
+
+
K
NR
K
N flow
R
N flow
R
()
F
N H
F
N flow
R
G
H
K
NR
,
0
1
,
2
1
1
,
:
+
+
=
TERMFL
TERMF2
TERMF1

Term
of exchange
()
K
N éch
R 1
,
+
()
()
.
100
1
,
1
,
×
+
+
K
NR
K
N éch
R
N éch
R
()
(
)
F
N H
ext.
F
N éch
R
HT
H
K
NR
,
0
1
,
2
1
1
,
:
+
+
=
TERMEC
TERME2
TERME1

Total
()
()
+
+
=
I
N I
R
N
R
K
K
1
,
1
:
()
()
.
100
1
1
×
+
+
K
NR
K
N
R
N
R
()
()
+
+
=
I
N I
R
N
R
K
NR
K
NR
1
,
1
:
ERTABS
ERTREL
TERMNO

For correct use, it is necessary to pay attention to the following points (cf R7.10.03 documentation):
·
preliminary call
“FLUX_ELNO_TEMP”
obligatory before the calculation of the indicators of errors;
·
homogeneity enters the parameter setting of the thermal solvor and the tool for postprocessing;
·
particular rules of overload concerning the loadings (generation of alarm
<A>
in
case of non-observance);
·
calculation on all the mesh associated with the model (generation with error
<F>
in the event of non-observance)
between two pitches of time contiguous or not (generation of alarm
<A>
in the event of non-observance);
·
all the elements 2D-plan/axi and 3D are treated (except
PYRAM
: generation of alarm
<A>
);
·
all the conditions limit except
ECHANGE_PAROI
,
FLUX_NL
and
RAYO
are taken into account
(
generation of alarm
<A>
in the event of use of
ECHANGE_PAROI
,
FLUX_NL
or
RAYO
);
·
the mesh tolerates the “outlines” but requires “to be cleaned a little” (not of
SEG/FACE
intercalated in surfaces/volumes, problem of symmetrization, points
double: generation of alarm
<A>
or of error
<F>)
.
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Code_Aster
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Version
6.4
Titrate:
Use of the indicators of error and strategies of adaptation
Date
:
17/10/03
Author (S):
P. BADEL, O. BOITEAU, V. CANO
Key
:
U2.08.01-A
Page
:
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HT-66/03/002/A
4.4
Adaptation of mesh with LOBSTER
The macro-control
MACR_ADAP_MAIL
controls itself with the following options:
_F Mot-clé
Choice
ADAPTATION
FREE
or
“RAFF_DERA”
“REFINEMENT”
“DERAFFINEMENT”
UNIFORM
“REFINEMENT”
“DERAFFINEMENT”
MAILLAGE_N/NP1
RESULTAT_N
INDICATOR
NOM_CMP_INDICA
“EVOL_NOLI” (*)
“ERRE_ELGA_NORE” (*)
“ERREST” (*)
CRIT_RAFF_PE
_REL
_ABS
CRIT_DERA_PE
_REL
_ABS
Allows to control the proportion of elements with
to refine/déraffiner
NIVE_MAX
NIVE_MIN
Max. level of refinement
Level min. of refinement
(*) example given on a non-linear calculation, use of the indicator in absolute residue.
Other possible options:
·
update of fields on the new mesh (
MAJ_CHAMP
); one cannot (still) put
up to date of the fields at the points of Gauss (like the variables intern for example);
·
diagnoses on the quality of the mesh (
QUALITY
,
INTERPENETRATION
,
CUT
,
CONNEXITY
).
Precautions for use:
·
adaptation of a total mesh (not of selection by meshs, groups of meshs, nodes,
group nodes);
·
the groups of meshs are adapted, on the other hand the groups of nodes are left
unchanged (it is thus necessary to be compelled to impose boundary conditions on groups of
meshs and not of the groups of nodes); it is thus necessary to proscribe (but it is a rule of good
feel) the direct use of meshs and nodes at the time them assignments to prefer the concept to him of
group meshs;
·
recoveries (by the key word
“CONTINUATION”
) are to be avoided: LOBSTER loses the hierarchy then
refined elements: the first mesh of the continuation is considered by LOBSTER
an initial mesh (without possibility of déraffiner for example);
·
it is reminded the meeting that the adaptation by LOBSTER accepts only nodes,
NOT
,
SEG
,
SORTED
or
TETRA
, of degree 1 or 2, in a mesh conforms in related areas or not, in the same way
dimension or not;
·
LOBSTER does not carry out yet the follow-up of curve (it bases itself on the provided elements: by
example, if the mesh of a circle is provided in the initial mesh by its approximation in
NR segments of command 1, LOBSTER will refine possibly the NR segments but the circle will be
always considering geometrically like a succession of these NR segments).
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Code_Aster
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Version
6.4
Titrate:
Use of the indicators of error and strategies of adaptation
Date
:
17/10/03
Author (S):
P. BADEL, O. BOITEAU, V. CANO
Key
:
U2.08.01-A
Page
:
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HT-66/03/002/A
4.5 Lookahead
of one
mesh
The diagnosis on the quality of a mesh activable in the macro one
MACR_ADAP_MAIL
can also be
obtained independently by the macro one
MACR_INFO_MAIL
. It makes it possible to carry out the checks
following:
·
to check the agreement of the mesh with the initial geometry (in mass, dimension, in
surface and in volume);
·
to list them
GROUP_MA
and
GROUP_NO
, for a good modeling of the boundary conditions;
·
to diagnose possible problems (symmetrization or connexity, elements of outline,
bad taking into account of boundary conditions, interpenetration of elements);
·
to evaluate the quality of the mesh by the indicator
K
K
K
H
=
(standardized to 1 for
equilateral triangles/tetrahedrons; by superior definition to 1). An empirical criterion can be
proposed: for example, at least 50% of EFs < 1.5, at least 90% of EFs < 2, not
elements with the top of 10.

5
The Councils and good practice
·
Choice of the indicator of error in mechanics: the user has the choice between ZZ1 (first version
indicator of Zhu-Zienkiewicz), ZZ2 (second version of the indicator of
Zhu-Zienkiewicz), and the indicator in residues. The two first have an applicability
enough reduces (2D linear for ZZ1 and ZZ2, only one standard of finite element in all the mesh
for ZZ2): for a “standard” use, one will prefer the indicator in residues.
·
The sequence “mechanical thermo operators/
MACR_ADAP_MAIL
option
“UNIFORM”
(i.e without indicator of error) allows to make converge properly, automatically and
easily a mesh. It is however necessary to take guard with the number of degrees of freedom
generated! This constitutes a solution of facility, rapid and robust, but quickly
extremely expensive (rather to reserve to evaluate if there are large errors of
discretization or for small studies).
·
The sequence “mechanical thermo operators/
MACR_ADAP_MAIL
option
“FREE”
(i.e with indicator of error) allows to make converge in the most optimal possible way
(taking into account the tools available) mesh. This method requires more efforts than
the preceding one but the number of generated degrees of freedom is proportionally much
weaker.
·
The sequence “mechanical thermo operators/
MACR_ADAP_MAIL
” can be carried out
effectively in a loop Python (of type “for loops”), with possibly a test of
exit (of type “while loops”).
·
The quality of the elements is impacted little by the process of refinement/déraffinement.
Taking into account the choices operated in LOBSTER
®
, it can even improve in 3D!
·
MACR_ADAP_MAIL
do not have process of regularization, therefore a bad mesh
initial a bad adapted mesh will probably produce!
·
The linear elements are disadvised in mechanics. The good practice is rather: P
1
lumpé in thermics (
PLAN_DIAG
,
AXIS_DIAG
,
3d_DIAG
) and P
2
(possibly
under-integrated) in mechanics, cf [bib9].
·
The choice of the type of finite elements premium on the quality of the meshs on which come
to rest the elements (cf example of the beam below).
·
The type of indicator and its mode of standardization can affect the mesh
adapted. For example, in mechanics,
()
()
()
2
,
0
2
100
K
H
rel
K
K
K
+
×
=
. This way of
to standardize can be dangerous: if there are areas where the standard of stresses is weak,
the error will border 100% on this area; if there are areas where the standard of stresses is
very high (singularities for example), the error will be weak on this area. It is not
obviously not the required result. It is thus necessary to use the absolute indicator preferably, with
less knowledge precisely than one makes.
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Code_Aster
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Version
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Titrate:
Use of the indicators of error and strategies of adaptation
Date
:
17/10/03
Author (S):
P. BADEL, O. BOITEAU, V. CANO
Key
:
U2.08.01-A
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:
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·
In thermics, one can also “juggle” with the components of the thermal indicator and of
boundary conditions, “fictitious” or not, to direct the construction of a refined mesh or
déraffiné by areas.
·
In the event of presence of singularities, it is advised to select the number of elements on
which refinement carries by a fraction of elements to refine
“CRIT_RAFF_PE”
(and not
not by the quantum of elements presenting a superior error at a fraction of the total error
“CRIT_RAFF_REL”
). Indeed, in the case of a singularity, by using `
CRIT_RAFF_REL
', with
boils of one or two iterations of adaptation, only the elements touching the singularity will be
refined. While using
“CRIT_RAFF_PE”
, other areas will be able to continue to be refined.
Finally the criterion
“CRIT_RAFF_ABS”
(choice by fixed barrier of error) is to be reserved for the cases where
the user knows the problem considered very well.
·
As a “simple postprocessing” of the thermomechanical problem, the indicator cannot
unfortunately not to provide a more reliable diagnosis in the areas where the resolution of
initial problem stumbles. It is thus preferable to begin a process of adjustment, with one
mesh refined already a little “with the hand”.
·
Into thermomechanical, various strategies of adaptation of mesh are offered to the user:
-
to only adapt the mesh according to a thermal criterion,
-
to only adapt the mesh according to a mechanical criterion,
-
to adapt jointly or separately (i.e with one or two loops of adaptation); in
clearly to chain or couple the first two strategies.
Good practice during such a thermomechanical calculation led to use two mesh and with
to interpolate the thermal field P
1
on the mechanical mesh P
2
(via the operator
PROJ_CHAMP
).
If one wishes to work only with one mesh, one can decline one of the strategies via
the option
MAJ_CHAMP
of
MACR_ADAP_MAIL
. That allows, while adapting the following mesh
a criterion, to update the complementary field on the new adapted mesh.
·
In thermics, to carry out an adaptation of mesh based on the indicator
ERTH_ELNO_ELEM
during a transient, one should not forget to start the calculation of the pitch
time following with the old one
EVOL_THER
updated on the new mesh.

6 Examples
of use
6.1
Mechanical example (beam 2D)
It is about a metal beam (steel 16MND5,
E
= 210.10
3
Mpa,
v
= 0.2) in bending. Calculation
rubber band (
MECA_STATIQUE
or
STAT_NON_LINE
) in modeling forced plane (
C_PLAN
).
Initial mesh in
TRIA3
or
TRIA6
.
X
10
GM12
PRES_REP=0.1 NR
GM14
GM1
3
DX=0
DY=0
Y
100
GM10
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Code_Aster
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Version
6.4
Titrate:
Use of the indicators of error and strategies of adaptation
Date
:
17/10/03
Author (S):
P. BADEL, O. BOITEAU, V. CANO
Key
:
U2.08.01-A
Page
:
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U2.08 booklet: Advanced function and control of calculations
HT-66/03/002/A
6.1.1 Use
of
MACR_INFO_MAIL
The macro one
MACR_INFO_MAIL
is launched in the command file by the following block. Mesh
is arranged here in a Python table:
MA [num_calc]
could be replaced by a name more
conventional in the absence of use of loops Python.
MACR_INFO_MAIL (MAILLAGE=MA [num_calc],
QUALITE=' OUI',
INTERPENETRATION=' OUI',
CONNEXITE=' OUI',
TAILLE=' OUI')
And one obtains in the file of message:
ANALYZE MESH
===================
Mesh has to analyze
MA_0
Creation date: Friday September 27, 2002 has 15. 58 mn 20 S
Dimension: 2
Degree: 1
It is a starting mesh.

Direction | Unit | Minimum | Maximum
--------------------------------------------------
X | UNKNOWN FACTOR | 0. | 100.00
Y | UNKNOWN FACTOR | 0. | 10.000

INTERPENETRATION OF THE ELEMENTS
=============================

**********************************************************
**
* Summary on the active faces *
**
* No problem was meets. *
**
**********************************************************

QUALITY OF THE ELEMENTS
====================
**********************************************************
* Quality of the triangles of the mesh of calculation *
* Recall: quality is equal to the report/ratio of the diameter *
* of the triangle on the radius of the inscribed circle, *
* standardizes has 1 for a regular triangle. *
**********************************************************
* Minimum: 1.0117 Maximum: 2.0158 *
**********************************************************

**********************************************************
* Function of distribution *
**
* Values * a Number of elements *
* Minicomputer < < Maximum * by class * office plurality *
** in %. numbers * in %. numbers *
**********************************************************
* 1.00 < 1.05 * 14.75. 9 * 14.75. 9 *
* 1.05 < 1.10 * 42.62. 26 * 57.38. 35 *
* 1.10 < 1.15 * 16.39. 10 * 73.77. 45 *
* 1.15 < 1.20 * 1.64. 1 * 75.41. 46 *
* 1.20 < 1.25 * 6.56. 4 * 81.97. 50 *
* 1.25 < 1.30 * 11.48. 7 * 93.44. 57 *
* 1.30 < 1.35 * 0.00. 0 * 93.44. 57 *
* 1.35 < 1.40 * 3.28. 2 * 96.72. 59 *
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Code_Aster
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Version
6.4
Titrate:
Use of the indicators of error and strategies of adaptation
Date
:
17/10/03
Author (S):
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* 1.40 < 1.45 * 0.00. 0 * 96.72. 59 *
* 1.45 < 1.50 * 0.00. 0 * 96.72. 59 *
* 1.50 < 1.55 * 0.00. 0 * 96.72. 59 *
* 1.55 < 1.60 * 0.00. 0 * 96.72. 59 *
* 1.60 < 1.65 * 0.00. 0 * 96.72. 59 *
* 1.65 < 1.70 * 0.00. 0 * 96.72. 59 *
* 1.70 < 1.75 * 1.64. 1 * 98.36. 60 *
* 1.75 < 1.80 * 0.00. 0 * 98.36. 60 *
* 1.80 < 1.85 * 0.00. 0 * 98.36. 60 *
* 1.85 < 1.90 * 0.00. 0 * 98.36. 60 *
* 1.90 < 1.95 * 0.00. 0 * 98.36. 60 *
* 1.95 < 2.00 * 0.00. 0 * 98.36. 60 *
* 2.00 < 2.05 * 1.64. 1 * 100.00. 61 *
* 2.05 < 2.10 * 0.00. 0 * 100.00. 61 *
* 2.10 < 2.15 * 0.00. 0 * 100.00. 61 *
* 2.15 < 2.20 * 0.00. 0 * 100.00. 61 *
* 2.20 < 2.25 * 0.00. 0 * 100.00. 61 *
* 2.25 < 2.30 * 0.00. 0 * 100.00. 61 *
* 2.30 < 2.35 * 0.00. 0 * 100.00. 61 *
* 2.35 < 2.40 * 0.00. 0 * 100.00. 61 *
* 2.40 < 2.45 * 0.00. 0 * 100.00. 61 *
* 2.45 < 2.50 * 0.00. 0 * 100.00. 61 *
* 2.50 < inf. * 0.00. 0 * 100.00. 61 *
**********************************************************


A NUMBER Of ENTITIES OF CALCULATION
==========================


**********************************************************
* Nodes *
**********************************************************
* Numbers total * 48 *
**********************************************************

**********************************************************
* Mesh-points *
**********************************************************
* Numbers total * 2 *
**********************************************************

**********************************************************
* Edges *
**********************************************************
* Total * 15 number *
*. of which edges isolees * 0 *
*. of which edges of edge of areas 2D * 15 *
*. of which edges intern with the faces/volumes * 0 *
**********************************************************
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Code_Aster
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Titrate:
Use of the indicators of error and strategies of adaptation
Date
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Key
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**********************************************************
* Faces *
**********************************************************
* Numbers total * 61 *
**********************************************************


CONNEXITY OF THE ENTITIES OF CALCULATION
===============================


**********************************************************
* The faces are in only one block. *
**********************************************************


SIZES OF THE SOUS-DOMAINES OF CALCULATION
===================================


Direction | Unit
-------------------------
X | UNKNOWN FACTOR
Y | UNKNOWN FACTOR

**********************************************************
* Under-fields 2D *
**********************************************************
* Number * Name * Surface *
**********************************************************
* - 4 * FAMILLE_MAILLE_-4_______________ * 1000.0 *
**********************************************************
* Total: * 1000.0 *
**********************************************************

**********************************************************
* 1D Under-fields *
**********************************************************
* Number * Name * Length *
**********************************************************
* - 3 * FAMILLE_MAILLE_-3_______________ * 10.000 *
* - 2 * FAMILLE_MAILLE_-2_______________ * 50.000 *
* - 1 * FAMILLE_MAILLE_-1_______________ * 40.000 *
**********************************************************
* Total: * 100.00 *
**********************************************************
One learns by this message:
·
extreme co-ordinates of the mesh;
·
the absence of problem of interpenetration;
·
a histogram of the geometrical quality of the elements (one will observe the good quality of it
mesh);
·
the number of nodes, meshs points, edges, faces;
·
the connexity of the mesh;
·
the size of the fields defined by the groups of meshs (this description is not very readable,
nevertheless, it will be observed that the field 2D of the beam is well of surface 1000 like
envisaged).
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6.1.2 Use
of
MACR_ADAP_MAIL
option
UNIFORM
In a loop Python, uniform refinement is required by the following call. Notice
important: a subtlety in the loops Python, it is necessary to declare the concept outgoing before using it
with the control
CO
.
# SUBTLETY MACRO_COMMANDE WITH RESPECT TO THE INPUTS
MA [num_calc1] =CO (“MA_ % of % (num_calc1))

# REFINEMENT UNIFORM VIA LOBSTER
# MESH STARTING: MA [num_calc]
# MESH Of ARRIVES: MA [num_calc1]
MACR_ADAP_MAIL (
ADAPTATION=_F (
UNIFORM = “REFINEMENT”,
MAILLAGE_N = MA [num_calc],
MAILLAGE_NP1 = MA [num_calc1],),
QUALITE=' OUI',
INTERPENETRATION=' OUI',
TAILLE=' OUI',
CONNEXITE=' OUI')
Let us observe the results obtained, by comparing a linear mesh (
TRIA3
) and a quadratic mesh
(
TRIA6
), initial mesh being presented on [Figure 6.1.2-a]. On the curves presenting the evolution
energy and arrow of the beam according to the number of refinement, cf [Figure 6.1.2-b] and
[Figure 6.1.2-c], two conclusions are essential:
·
on the one hand the quadratic elements show their obvious superiority;
·
in addition, mending of meshes (here very simplistic since it is uniform) proves its interest:
initial linear mesh being very far from being sufficiently refined, mending of meshes makes it possible to obtain
good results after some iterations.
Appear 6.1.2-a: initial Mesh
Appear 6.1.2-b: Evolution of energy with
the number of refinements
Appear 6.1.2-c: Evolution of the arrow with
the number of refinements
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6.1.3 Use
of
MACR_ADAP_MAIL
option
FREE
The first question to regulate during the use of free refinement with LOBSTER is the choice of
the indicator of error and its component. Here, according to the principles stated in the paragraph of
consultings, the choice was made use the indicator in residue (even if in this case, one is in
perimeter of use of the indicators of Zhu-Zienkiewicz). On the other hand, this example compares them
components absolute and standardized indicator in order to illustrate the prudence which the use imposes of
the standardized component.
The mesh is here linear in order to clearly illustrate the effect of the adaptation of mesh, because one saw
previously that the initial mesh gives already results of good quality with elements
of command 2.
Free refinement on the absolute component (for the relative component, it is enough to change in
the extract below
NOM_CMP_INDICA=' ERREST'
in
NOM_CMP_INDICA=' NUEST'
) is activated by
following controls:
# SUBTLETY MACRO_COMMANDE WITH RESPECT TO THE INPUTS
MA [num_calc1] =CO (“MA_ % of % (num_calc1))

# REFINEMENT FREE VIA LOBSTER
# MESH STARTING: MA [num_calc]
# MESH Of ARRIVES: MA [num_calc1]
MACR_ADAP_MAIL (
ADAPTATION=_F (
FREE = “RAFF_DERA”,
MAILLAGE_N = MA [num_calc],
MAILLAGE_NP1 = MA [num_calc1],
RESULTAT_N=DEPLA [num_calc],
INDICATEUR=' ERRE_ELGA_NORE',
NOM_CMP_INDICA=' ERREST',
CRIT_RAFF_PE=0.2,
CRIT_DERA_PE=0.2),
QUALITE=' OUI',
INTERPENETRATION=' OUI',
TAILLE=' OUI',
CONNEXITE=' OUI')


If one compares the results on the arrow with
“absolute” component and the “relative” component
according to the number of nodes (cf [Figure 6.1.3-a]
where one added the same evolution for refinement
uniform), one observes:
·
free refinement with the component
absolute converges more quickly towards the reference
that uniform refinement (from where interest of
to make free refinement);
·
free refinement with the component
relative converges more slowly towards
reference that uniform refinement, which
is at first sight surprising.
Appear 6.1.3-a: Evolution of energy in
function of the number of nodes
This last point is explained if one traces the three fields from the indicator of error, which is made on
[Figure 6.1.3-b] - [Figure 6.1.3-d].
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Appear absolute Component 6.1.3-b:
Appear 6.1.3-c: Stress of standardization normalizes
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Appear 6.1.3-d: Standardized component
It appears clearly that the fact that the standard of the standardized stress is weak in an area
(neutral fiber of the beam in particular) where refinement is less necessary than elsewhere (see the error
absolute) the result of standardization returns
()
()
()
2
,
0
2
100
K
H
rel
K
K
K
+
×
=
random. Indeed,
it is reminded the meeting that areas with stress of null standardization will be regarded as having one
error of 100%: if it is necessary to refine in this area, that will be good (though that will mask the others
areas to refine), if refinement is less necessary, that will be bad. It is thus necessary well to analyze
its problem before using the relative component of the indicator of error, the absolute component
being able to be regarded as surer. In particular, it seems to us that the use of the error
standardized is not possible that after analysis by the user of the card of stress of standardization.

6.2
Thermoelastic example (simplified cylinder head)
The following structure is considered:
8
20
Y
55
X
3
10
3
4
6
3
3
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subjected to the following loadings:
GM36
ECHANGE= (1000 W/m
2
°C,
350
°C)
Y
X
GM37
ECHANGE= (5000 W/m
2
°C,
150
°C)
GM33
OUTGOING FLOW
=-400 W/m
2
GM35
GM39/GM40
DX=DY=0
GM34
PRES_REP= 0.1N

Initially, one is interested in thermics only to underline the possibility of using
decomposition of the various terms of error. Indeed, within the framework of a “standard” use
(i.e. when all the terms of error interest the user), will have to be chosen the total error
(
“ERTABS”
or
“ERTREL”
); on the other hand, if the user is particularly interested by good
taking into account of the boundary conditions, it can thus direct refinement by using the different ones
terms (of flow or exchange in this case). For example, on the basis of the mesh [Figure 6.2-a] - one
will note that this mesh checks one of our consultings which is to start from a “reasonable” mesh - one
carry out a refinement on the relative total error, cf the result [Figure 6.2-b]:
# MESH STARTING: CHECHMATE [num_calc]
# MESH Of ARRIVES: CHECHMATE [num_calc1]
MACR_ADAP_MAIL (
ADAPTATION=_F (
FREE = “RAFF_DERA”,
MAILLAGE_N = CHECHMATE [num_calc],
MAILLAGE_NP1 = CHECHMATE [num_calc1],
RESULTAT_N=TEMP [num_calc],
INDICATEUR=' ERTH_ELEM_TEMP',
NOM_CMP_INDICA=' ERTREL',
CRIT_RAFF_PE=0.1,
CRIT_DERA_PE=0.1,
),
QUALITE=' OUI',
INTERPENETRATION=' OUI',
TAILLE=' OUI',
CONNEXITE=' OUI')
and a refinement on the term of exchange, cf the result appears (10):
# MESH STARTING: CHECHMATE [num_calc]
# MESH Of ARRIVES: CHECHMATE [num_calc1]
MACR_ADAP_MAIL (
ADAPTATION=_F (
FREE = “RAFF_DERA”,
MAILLAGE_N = CHECHMATE [num_calc],
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MAILLAGE_NP1 = CHECHMATE [num_calc1],
RESULTAT_N=TEMP [num_calc],
INDICATEUR=' ERTH_ELEM_TEMP',
NOM_CMP_INDICA=' TERME2',
CRIT_RAFF_PE=0.1,
CRIT_DERA_PE=0.1,
),
QUALITE=' OUI',
INTERPENETRATION=' OUI',
TAILLE=' OUI',
CONNEXITE=' OUI')
It is observed obviously that the adapted mesh strongly differs. In the second case of
appear, refinement was indeed directed towards drillings, seats of the conditions of exchanges.
Appear 6.2-a: initial Mesh
Appear 6.2-b: Mesh refined starting from the relative total error
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Appear 6.2-c: Mesh refined starting from the relative error on the term of exchange
One is interested now in coupled elastic thermo calculation. This problem remains rather simple since it
one pitch of time has there. According to the consultings given previously, one carries out this calculation
coupled on two different mesh: a “thermal” mesh linear on which will be based
lumpés elements and a “mechanical” mesh quadratic, the passage of the one with the other being carried out
by the operator
“PROJ_CHAMP”
.
More precisely: with each stage of the loop of refinement, one starts by calculating
temperature on the thermal mesh:
TEMP [num_calc] =THER_LINEAIRE (
MODELE=MOT [num_calc],
CHAM_MATER=CHMATT [num_calc],
EXCIT= (
_F (LOAD = CHT [num_calc]),
_F (LOAD = CLIMT [num_calc],),)
)
then one projects this temperature on the mechanical mesh (one created a model beforehand
thermics
MOT2
dependant on the mechanical mesh):
TEMP2 [num_calc] =PROJ_CHAMP (
METHODE=' ELEM',
RESULTAT=TEMP [num_calc],
MODELE_1=MOT [num_calc],
MODELE_2=MOT2 [num_calc],
TOUT_ORDRE=' OUI')
One uses this temperature under the boundary conditions of mechanical calculation:
CLIMM [num_calc] =AFFE_CHAR_MECA (
MODELE=MOM [num_calc],
TEMP_CALCULEE=TEMP2 [num_calc],
DDL_IMPO= (_F (GROUP_NO=' GM39', DX=0.0, DY=0.0),
_F (GROUP_NO=' GM40', DX=0.0, DY=0.0),),)
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mechanical calculation is carried out:
DEPLA [num_calc] =STAT_NON_LINE (MODELE=MOM [num_calc],
CHAM_MATER=CHMATM [num_calc],
EXCIT= (_F (CHARGE=CLIMM [num_calc],),
_F (CHARGE=CHM [num_calc],
FONC_MULT=F_INST,),),
COMP_INCR= (_F (RELATION=' ELAS',
TOUT=' OUI',),),
INCREMENT=_F (LIST_INST=L_INST),)
One calculates the indicators of thermal and mechanical error:
TEMP [num_calc] =CALC_ELEM (reuse=TEMP [num_calc],
RESULTAT=TEMP [num_calc],
MODELE=MOT [num_calc],
TOUT=' OUI',
TOUT_ORDRE=' OUI',
CHAM_MATER=CHMATT [num_calc],
EXCIT= (
_F (LOAD = CHT [num_calc]),
_F (LOAD = CLIMT [num_calc],),),
OPTION= (
“FLUX_ELNO_TEMP”,
“ERTH_ELEM_TEMP”,
“ERTH_ELNO_ELEM”,),)

DEPLA [num_calc] =CALC_ELEM (reuse=DEPLA [num_calc],
RESULTAT=DEPLA [num_calc],
MODELE=MOM [num_calc],
TOUT=' OUI',
CHAM_MATER=CHMATM [num_calc],
EXCIT= (_F (CHARGE=CLIMM [num_calc],),
_F (CHARGE=CHM [num_calc],),),
TOUT_ORDRE=' OUI',
OPTION= (
“SIEF_ELNO_ELGA”,
“ERRE_ELGA_NORE”,),)
then one connects with the adaptation of the thermal and mechanical mesh
MACR_ADAP_MAIL (
ADAPTATION=_F (
FREE = “RAFF_DERA”,
MAILLAGE_N = CHECHMATE [num_calc],
MAILLAGE_NP1 = CHECHMATE [num_calc1],
RESULTAT_N=TEMP [num_calc],
INDICATEUR=' ERTH_ELEM_TEMP',
NOM_CMP_INDICA=' ERTREL',
CRIT_RAFF_PE=0.1,
CRIT_DERA_PE=0.1,
),
QUALITE=' OUI',
INTERPENETRATION=' OUI',
TAILLE=' OUI',
CONNEXITE=' OUI')
MACR_ADAP_MAIL (
ADAPTATION=_F (
FREE = “RAFF_DERA”,
MAILLAGE_N = MAM [num_calc],
MAILLAGE_NP1 = MAM [num_calc1],
RESULTAT_N=DEPLA [num_calc],
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INDICATEUR=' ERRE_ELGA_NORE',
NOM_CMP_INDICA=' NUEST',
CRIT_RAFF_PE=0.1,
CRIT_DERA_PE=0.1,
),
QUALITE=' OUI',
INTERPENETRATION=' OUI',
TAILLE=' OUI',
CONNEXITE=' OUI')
Before starting again at the following stage…
6.3 Example
thermo plastic
One considers the structure of following revolution (modelized into axisymmetric):
where the grayed parts are plastic, the elastic remainder. The loading is applied in 2 stages:
·
the first consists of a purely mechanical loading (pressure on the area with
arrows on the diagram), with a phase of load followed by a phase of discharge;
·
the second consists of a transitory thermal loading (condition of exchange on
lower parts and higher of the structure).
6.3.1 Strategy of mending of meshes and list of moments
The loading is discretized according to a list of moments, it raises the question then: which strategy
to adopt with respect to mending of meshes? Indeed, according to the treated case, one can:
·
to re-mesh with each pitch of calculation: the mesh is then adapted to each pitch of calculation
individually. It is then necessary to project the fields of a mesh on the other (what is not
still completely possible in non-linear mechanics);
·
to re-mesh only once, at the end it calculation, and to start again calculation since the beginning with
new mesh.
The first strategy is to be adopted if the areas of refinement evolve/move much, us
in will see an example in following thermal calculation; the second can be adopted if
the areas of refinement evolve/move little, as in this mechanical case where it is a question of following
growth of a plastic area.
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6.3.2 Calculation
mechanics
For mechanical calculation, one thus adopts the following strategy:
1) calculation of all the list of moments;
2) mending of meshes
;
3) repetition of (1 & 2) until the satisfactory result.
It is not so much the implementation in Aster which is interesting in this case (which differs from the settings
in work the preceding ones only by the fact that several moments ago of calculation) that the results
obtained by adaptation of mesh on a non-linear case. For recall, calls for calculation
indicators of error and for mending of meshes are as follows:
V1 [num_calc] =CALC_ELEM (reuse =V1 [num_calc],
MODELE=MO1 [num_calc],
CHAM_MATER=CM1 [num_calc],
INST=-1.0,
OPTION= (“ERRE_ELGA_NORE”,),
RESULTAT=V1 [num_calc],)
MA [num_calc+1] =CO (“MA_ % of % (num_calc+1))

MACR_ADAP_MAIL (
ADAPTATION=_F (
FREE = “REFINEMENT”,
MAILLAGE_N = MA [num_calc],
MAILLAGE_NP1 = MA [num_calc+1],
RESULTAT_N = V1 [num_calc],
INDICATOR = “ERRE_ELGA_NORE”,
NOM_CMP_INDICA=' ERREST',
NUME_ORDRE = 4,
CRIT_RAFF_PE = 0.1,
NIVE_MAX = 5),
QUALITE=' OUI',
INTERPENETRATION=' NON',
TAILLE=' OUI',
CONNEXITE=' OUI'
)
To judge contribution of mending of meshes, let us look at the radial stresses on the segment indicated on
[Figure 6.3.2-a], which is compared with a “reference” obtained by 3 uniform mendings of meshes: gain
the mendings of meshes based on the indicator of error is visible.
Line of postprocessing
Appear 6.3.2-a: Place of postprocessing
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Appear 6.3.2-b: Profile of stress

One will find on the figures [Figure 6.3.2-c] and [Figure 6.3.2-d] the initial mesh and the mesh after 3
mendings of meshes based on the indicator of error.

An indication of the size (and thus of the time) of calculations between the calculation of reference (3 refinements
uniforms) and calculation with 3 refinements based on the indicator of error is given in the table
[Table 6.3.2-1].

A number of nodes
Calculating time
Mesh of reference
175 000
~3000 S
3 free refinements (either 4 calculations)
8 500
~60 S
Table 6.3.2-1: indication of performances
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Appear 6.3.2-c: Initial mesh
Appear 6.3.2-d: Mesh after 3 mendings of meshes
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6.3.3 Calculation of the thermal transient
It is a question in this calculation case a thermal transient, two conditions of exchanges being imposed
in bottom and top of the structure. As the area which will present a strong variation in temperature goes
to move in the structure (projection of a face), the strategy adopted for mending of meshes will hold some
count: it is necessary to reactualize the mesh during the transient regularly. In practice, one subdivides
the list of moments in blocks, inside these blocks of moments of calculation the mesh will be the same one (and it
mending of meshes intervenes at the end of the block). There are thus 3 overlapping loops:
1) the loop on the NR blocks of moments;
2) the loop on mendings of meshes of the current block;
3) the loop (hidden in
THER_LINEAIRE
) over the moments of the block.
That gives in the command file:
for num_inst_raff in arranges (1, nb_raff-1):
The loop on the blocks of moments
num_inst_debut = (num_inst_raff-1) * pas_raff+1
num_inst_fin = (num_inst_raff) * pas_raff

for num_calc in arranges (1, nb_calc-1):
The loop on mendings of meshes
yew (num_calc == 1) gold (num_inst_raff == 1):

yew (num_inst_raff == 1):
If it is about the first block, one thus begins a calculation (not “
reuse
”)
EV [I] =THER_LINEAIRE (MODELE=MOTH [I],
CHAM_MATER=CHMAT [I],
EXCIT= (_F (CHARGE=CHBF [I],),
_F (CHARGE=CHFL [I],),),
INCREMENT=_F (LIST_INST=LIST,
NUME_INIT=num_inst_debut-1,
NUME_FIN=num_inst_fin,),)
else:
If it is about the initial mesh of the block of moment (i.e. the last mesh of the block of moment
precedent), one again did not create mesh (one thus did not carry out
PROJ_CHAMP
) and it is necessary
to go to seek the initial temperature in the result of the preceding block (last moment of the block
precedent):
EV [I] =THER_LINEAIRE (reuse=EV [I],
MODELE=MOTH [I],
CHAM_MATER=CHMAT [I],
TEMP_INIT=_F (EVOL_THER=EV [I],
NUME_INIT=num_inst_debut-1,
),
EXCIT= (_F (CHARGE=CHBF [I],),
_F (CHARGE=CHFL [I],),),
INCREMENT=_F (LIST_INST=LIST,
NUME_INIT=num_inst_debut-1,
NUME_FIN=num_inst_fin,),)
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Code_Aster
®
Version
6.4
Titrate:
Use of the indicators of error and strategies of adaptation
Date
:
17/10/03
Author (S):
P. BADEL, O. BOITEAU, V. CANO
Key
:
U2.08.01-A
Page
:
25/30
Instruction manual
U2.08 booklet: Advanced function and control of calculations
HT-66/03/002/A
Lastly, if it is about a mending of meshes, one will seek the initial temperature in one
CHAM_NO
calculated with
moment of mending of meshes (cf further mending of meshes):
else:
EV [I] =THER_LINEAIRE (
MODELE=MOTH [I],
CHAM_MATER=CHMAT [I],
TEMP_INIT = _F (CHAM_NO = CT),
EXCIT= (_F (CHARGE=CHBF [I],),
_F (CHARGE=CHFL [I],),),
INCREMENT=_F (LIST_INST=LIST,
NUME_INIT=num_inst_debut-1,
NUME_FIN=num_inst_fin,),)
yew num_calc!= (nb_calc-2):
It is necessary to re-mesh…
One starts by calculating the indicator of error:
EV [I] =CALC_ELEM (reuse=EV [I],
NUME_ORDRE=num_inst_fin,
RESULTAT=EV [I],
MODELE=MOTH [I],
TOUT=' OUI',
CHAM_MATER=CHMAT [I],
EXCIT= (_F (CHARGE=CHBF [I],),
_F (CHARGE=CHFL [I],),),
OPTION= (
“FLUX_ELNO_TEMP”,
“ERTH_ELEM_TEMP”,
“ERTH_ELNO_ELEM”,),)
MATHS [i+1] =CO (“MATH_ % of % (i+1))

yew (detr_ct == 1):
TO DESTROY (CONCEPT=_F (NOM=' CT',),)

yew num_inst_raff == 1:
If the first block is treated, there is no field of temperature to project on the new mesh:
MACR_ADAP_MAIL (
ADAPTATION=_F (
FREE = “RAFF_DERA”,
MAILLAGE_N = MATHS [I],
MAILLAGE_NP1 = MATHS [i+1],
RESULTAT_N=EV [I],
INDICATEUR=' ERTH_ELEM_TEMP',
NUME_ORDRE = num_inst_fin,
NOM_CMP_INDICA=' ERTREL',
CRIT_RAFF_PE=0.03,
CRIT_DERA_PE=0.2,
NIVE_MAX=4,
),
QUALITE=' OUI',
INTERPENETRATION=' OUI',
TAILLE=' OUI',
CONNEXITE=' OUI')

else:
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Code_Aster
®
Version
6.4
Titrate:
Use of the indicators of error and strategies of adaptation
Date
:
17/10/03
Author (S):
P. BADEL, O. BOITEAU, V. CANO
Key
:
U2.08.01-A
Page
:
26/30
Instruction manual
U2.08 booklet: Advanced function and control of calculations
HT-66/03/002/A
if the block of moment is not the first, it is necessary to project the temperature of the last moment of calculation of
preceding block in one
CHAM_NO
(called here
“CT”
) in order to use it
CHAM_NO
like temperature
initial on the new mesh:
MACR_ADAP_MAIL (
ADAPTATION=_F (
FREE = “RAFF_DERA”,
MAILLAGE_N = MATHS [I],
MAILLAGE_NP1 = MATHS [i+1],
RESULTAT_N=EV [I],
INDICATEUR=' ERTH_ELEM_TEMP',
NUME_ORDRE = num_inst_fin,
NOM_CMP_INDICA=' ERTREL',
CRIT_RAFF_PE=0.03,
CRIT_DERA_PE=0.2,
NIVE_MAX=4,
),
MAJ_CHAM=_F (
RESULTAT= (“EV_ % of % (I)),
NOM_CHAM=' TEMP',
NUME_ORDRE=num_inst_debut-1,
CHAM_MAJ=CO (“CT”),
TYPE_CHAM=' CHAM_NO_TEMP_R',
),
QUALITE=' OUI',
INTERPENETRATION=' OUI',
TAILLE=' OUI',
CONNEXITE=' OUI')

detr_ct = 1

i=i+1
One defines the concepts Aster members in the mesh:
MOTH [I] =AFFE_MODELE (
MAILLAGE=MATH [I],
AFFE=_F (TOUT=' OUI',
PHENOMENE=' THERMIQUE',
MODELISATION=' AXIS_DIAG',),)
#---------------- REORIENTATION OF GROUPS OF EDGE
#


MATHS [I] =MODI_MAILLAGE (reuse =MATH [I],
MAILLAGE=MATH [I],
ORIE_PEAU_2D=_F (GROUP_MA= (“GM58”, “GM42”,
“GM45”, “GM57”, “GM56”),),
MODELE=MOTH [I],
INFO=1,);
#--------- ASSIGNMENT THERMAL CHARACTERISTICS ------
#
CHMAT [I] =AFFE_MATERIAU (MAILLAGE=MATH [I],
AFFE= (_F (GROUP_MA= (“GM47”, “GM48”),
MATER=MATHPL,
TEMP_REF=20.0,),
_F (GROUP_MA= (“GM46”),
MATER=MATHBO,
TEMP_REF=20.0,),),)
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Code_Aster
®
Version
6.4
Titrate:
Use of the indicators of error and strategies of adaptation
Date
:
17/10/03
Author (S):
P. BADEL, O. BOITEAU, V. CANO
Key
:
U2.08.01-A
Page
:
27/30
Instruction manual
U2.08 booklet: Advanced function and control of calculations
HT-66/03/002/A
CHFL [I] =AFFE_CHAR_THER_F (MODELE=MOTH [I],
FLUX_REP=_F (GROUP_MA= (“GM57”,),
FLUN=ZERO,),)
# LOADING EXCHANGE ON PLATE Lower Side
# CONNECTS COLD - HOT BRANCH
#


CHBF [I] =AFFE_CHAR_THER_F (MODELE=MOTH [I],
ECHANGE= (_F (GROUP_MA= (“GM45”,),
COEF_H=HP,
TEMP_EXT=TBF,),
_F (GROUP_MA= (“GM42”, “GM58”),
COEF_H=HB,
TEMP_EXT=TBF,),),)

# LOADING EXCHANGE ON PLATE Higher Side
# SHOCK 4TH CATEGORY
#


CHTS4 [I] =AFFE_CHAR_THER_F (MODELE=MOTH [I],
ECHANGE=_F (GROUP_MA= (“GM56”),
COEF_H=HS,
TEMP_EXT=TS4,),)

If one looks at the results at the last moment calculated, in particular the temperature on the line of post-
processing already used in mechanics, cf [Figure 6.3.3-c], one notes the interest of the adaptation of
mesh. As one will be able to note it on the mesh initial and adapted (with the last pitch of time),
Cf [Figure 6.3.3-a] ­ [Figure 6.3.3-b], the mesh did not change in the vicinity close to this line of
examination: the improvement of the calculated temperature comes from the areas that one refined by
elsewhere. It will be also noticed that the refined mesh is not very intuitive: it is there too about one of
interest of the automatic adaptation of mesh.
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Code_Aster
®
Version
6.4
Titrate:
Use of the indicators of error and strategies of adaptation
Date
:
17/10/03
Author (S):
P. BADEL, O. BOITEAU, V. CANO
Key
:
U2.08.01-A
Page
:
28/30
Instruction manual
U2.08 booklet: Advanced function and control of calculations
HT-66/03/002/A
Appear 6.3.3-a: initial Mesh
Appear 6.3.3-b: Mesh refined in the last
no calculating time
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Code_Aster
®
Version
6.4
Titrate:
Use of the indicators of error and strategies of adaptation
Date
:
17/10/03
Author (S):
P. BADEL, O. BOITEAU, V. CANO
Key
:
U2.08.01-A
Page
:
29/30
Instruction manual
U2.08 booklet: Advanced function and control of calculations
HT-66/03/002/A
Appear 6.3.3-c: Profile of temperature
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Code_Aster
®
Version
6.4
Titrate:
Use of the indicators of error and strategies of adaptation
Date
:
17/10/03
Author (S):
P. BADEL, O. BOITEAU, V. CANO
Key
:
U2.08.01-A
Page
:
30/30
Instruction manual
U2.08 booklet: Advanced function and control of calculations
HT-66/03/002/A


























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