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Organization (S): EDF-R & D/AMA, SINETICS
Handbook of Utilization
U2.08 booklet: Advanced functions and control of calculations
Document: U2.08.01
Use of the indicators of error and strategies
of adaptation of grids associated

Summary:

This document describes the use in Code_Aster of the indicators of error and their use in a context
of adaptation of grid. 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 grids: 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.

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1 Introduction

The indicators of error and the adaptation of grids 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 grid
is carried out by call to an external program, specialized in this task, HOMARD.
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 grids;
4) a recall of the commands 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 grid is delimited by
following constraints (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 grids made up either of triangles or of
quadrangles); on the other hand, the use of the adaptation of grids with HOMARD requires
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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3 References
useful

The documents [bib1] with [bib5] estimators of error and tool for adaptation of grid treat
HOMARD.
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-command MACR_ADAP_MAIL”. Doc. [U7.03.01].
[6]
O. BOITEAU: Case-test. “Mechanical FORMA04 ­ adaptive Maillage on a beam in
inflection “. Doc. [V6.03.119]
[7]
O. BOITEAU: Case-test. “FORMA05 ­ thermomechanical adaptive Maillage on a bolt
fissured “. Doc. [V6.03.120]
[8]
O. BOITEAU: Run and TP “Indicateurs of error and adaptation of grid. 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 language Aster the process control (based
on Python) adapted to this use.

1) Definition of the data of calculation (in
1) Definition of the data of calculation (in
private individual grid)
private individual initial grid)
2) Resolution of the problem
2) Resolution of the problem
3) Calculation of the indicators of error (post-
3) Calculation of the indicators of error (post-
processing)
processing)
4) Adaptation of the grid (based on one of
indicators calculated at stage 3)
Use of the indicators of error
Use of the adaptation of grid

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4
Recall of the commands and Aster options 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 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 constraints 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);
K
“NUEST”: the relative error estimated on the element rel (K)
()
= 100×
;
(K) 2
2
+ H 0, K
“SIGCAL”: the standard of energy of the calculated solution H
;
0, K

· output-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
constraints to normalize the error, by operator CALC_ELEM:
OPTION= `SIGM_ELNO_DEPL' in elasticity (after MECA_STATIQUE);
OPTION= `SIEF_ELNO_ELGA' into non-linear (after STAT_NON_LINE).

The calculation of the estimator of error itself is also carried out in 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);
K
“NUEST”: the relative error estimated on the element rel (K)
()
= 100×
;
(K) 2
2
+ H 0, K
“SIGCAL”: the standard of energy of the calculated solution H
.
0, K

· output-listing comprising same information at the total level.
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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 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

N 1
+

N 1
+

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

n+
NR R, flight (K)
.
100
1





TERMVO
TERMV2
TERMV1

N 1
+

N 1
+

1
R, jump (K)
R, jump (K)
Term of jump
×
N 1
2
+
N 1
H
+
1
T

F
, H

n+
NR, jump (K):=

(K)
NR R jump (K)
.
100
1
,
2 2
N

K

F
0, F



TERMSA
TERMS2
TERMS1

N 1
+

N 1
+

1
R, flow (K)
R, flow (K)
Term of flow
×100
N
NR 1
+
2
1
+
R, flow (K)
N
:= H G


N 1
+
NR
F
, H
R, flow (K)
.
0, F



TERMFL
TERMF2
TERMF1

N 1
+

N 1
+

1
R, éch (K)
R, éch (K)
Term
×
N
NR 1
+
2
1
+
R, éch (K):= HF (
ext.
HT) N
of exchange

n+
NR
, H
R éch (K)
.
100
1
,
0, F


TERMEC
TERME2
TERME1

n+1
1

n+

n+
NR 1
1
R
(K) =: n+
NR R I, (K)
R (
1 K)
R (K) =
: n+
R I, (K)

Total
×

I
n+
NR
I
R
(K)
.
100
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 grid associated with the model (generation of <F> error in the event of non-observance)
between two steps 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 limiting conditions 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 grid 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 <F> error).
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4.4
Adaptation of grid with HOMARD

Macro-command MACR_ADAP_MAIL is controlled with the following options:

_F Word-key
Choice
ADAPTATION
LIBRE
“RAFF_DERA”

“RAFFINEMENT”
or
“DERAFFINEMENT”


UNIFORME
“RAFFINEMENT”
“DERAFFINEMENT”

MAILLAGE_N/NP1


RESULTAT_N
“EVOL_NOLI” (*)
INDICATEUR
“ERRE_ELGA_NORE” (*)
NOM_CMP_INDICA
“ERREST” (*)

CRIT_RAFF_PE
Allows to control the proportion of elements with
_REL
to refine/déraffiner
_ABS
CRIT_DERA_PE
_REL
_ABS


NIVE_MAX
Max. level of refinement
NIVE_MIN
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 new grid (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 grid (QUALITE, INTERPENETRATION, TAILLE, CONNEXITE).

Precautions for use:
· adaptation of a total grid (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;
· the recoveries (by key word “POURSUITE”) are to be avoided: HOMARD loses the hierarchy then
refined elements: the first grid of the continuation is considered by HOMARD
an initial grid (without possibility of déraffiner for example);
· it is pointed out that the adaptation by HOMARD accepts only nodes, POINT, SEG, TRIA or
TETRA, of degree 1 or 2, in a grid conforms in related zones or not, in the same way
dimension or not;
· HOMARD does not carry out yet the follow-up of curve (it is based on the provided elements: by
example, if the grid of a circle is provided in the initial grid by its approximation in
NR segments of command 1, HOMARD 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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4.5 Lookahead
of one
grid

The diagnosis on the quality of a grid activable in the macro MACR_ADAP_MAIL can also be
obtained independently by the macro MACR_INFO_MAIL. It makes it possible to carry out the checks
following:
· to check the agreement of the grid with the initial geometry (in mass, dimension, in
surface and in volume);
· to list the 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);
H
· to evaluate the quality of the grid by the indicator
K
K =
(standardized to 1 for
K
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 grid
for ZZ2): for a “standard” use, one will prefer the indicator in residues.
· The sequence “mechanical thermo operators/MACR_ADAP_MAIL option “UNIFORME””
(i.e without indicator of error) allows to make converge properly, automatically and
easily a grid. 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 “LIBRE””
(i.e with indicator of error) allows to make converge in the most optimal possible way
(taking into account the tools available) grid. This method requires more efforts than
the preceding one but the number of generated degrees of freedom is proportionally much
weaker.
· The sequence “thermo operators mechanical/MACR_ADAP_MAIL” can be carried out
effectively in a Python loop (of type “for loops”), with possibly a test of
output (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 HOMARD®, it can even improve in 3D!
· MACR_ADAP_MAIL does not have process of regularization, therefore a bad grid
initial a bad adapted grid will probably produce!
· The linear elements are disadvised in mechanics. The good practice is rather: P1
lumpé in thermics (PLAN_DIAG, AXIS_DIAG, 3d_DIAG) and P2 (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 grid
K
adapted. For example, in mechanics, rel (K)
()
= 100×
. This way of
(K) 2
2
+ H 0, K
to standardize can be dangerous: if there are zones where the standard of constraints is weak,
the error will border 100% on this zone; if there are zones where the standard of constraints is
very high (singularities for example), the error will be weak on this zone. 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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· 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 grid or
déraffiné by zones.
· 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. By using “CRIT_RAFF_PE”, other zones will be able to continue to be refined.
Finally criterion “CRIT_RAFF_ABS” (choice by fixed barrier of error) is to be held 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 zones where the resolution of
initial problem stumbles. It is thus preferable to begin a process of adjustment, with one
grid refined already a little “with the hand”.
· Into thermomechanical, various strategies of adaptation of grid are offered to the user:
- to only adapt the grid according to a thermal criterion,
- to only adapt the grid 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 grids and with
to interpolate the thermal field P1 on the mechanical grid P2 (via operator PROJ_CHAMP).
If one wishes to work only with one grid, one can decline one of the strategies via
option MAJ_CHAMP of MACR_ADAP_MAIL. That allows, while adapting the following grid
a criterion, to update the complementary field on the new adapted grid.
· In thermics, to carry out an adaptation of grid based on the indicator
ERTH_ELNO_ELEM during a transient, one should not forget to start the calculation of the step
time following with the old EVOL_THER updated on the new grid.

6 Examples
of use

6.1
Mechanical example (beam 2D)

It is about a metal beam (steel 16MND5, E = 210.103 Mpa, v = 0.2) in inflection. Calculation
rubber band (MECA_STATIQUE or STAT_NON_LINE) in modeling forced plane (C_PLAN).
Initial grids in TRIA3 or TRIA6.

GM12
PRES_REP=0.1 NR
Y
GM14
X
10
GM13
DX=0
GM10
DY=0
100

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6.1.1 Use
of
MACR_INFO_MAIL

The macro MACR_INFO_MAIL is launched in the command file by the following block. Grid
is arranged here in a Python table: MA [num_calc] could be replaced by a name more
conventional in the absence of use of Python loops.
MACR_INFO_MAIL (MAILLAGE=MA [num_calc],
QUALITE=' OUI',
INTERPENETRATION=' OUI',
CONNEXITE=' OUI',
TAILLE=' OUI')

And one obtains in the file of message:
ANALYZE GRID
===================
Grid 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 grid.

Direction | Unit | Minimum | Maximum
--------------------------------------------------
X | INCONNUE | 0. | 100.00
Y | INCONNUE | 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 grid 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 * Nombre of elements *
* Minicomputer < < Maxi * 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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* 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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**********************************************************
* 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 | INCONNUE
Y | INCONNUE

**********************************************************
* 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 grids;
· the absence of problem of interpenetration;
· a histogram of the geometrical quality of the elements (one will observe the good quality of it
grid);
· the number of nodes, meshs points, edges, faces;
· the connexity of the grid;
· 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 UNIFORME

In a Python loop, 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 command CO.
# SUBTLETY MACRO_COMMANDE WITH RESPECT TO THE INPUTS
MA [num_calc1] =CO (“MA_ % of % (num_calc1))

# REFINEMENT UNIFORM VIA LOBSTER
# GRID STARTING: MA [num_calc]
# GRID 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 grid (TRIA3) and a quadratic grid
(TRIA6), initial grid 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 grid 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 Maillage


Appear 6.1.2-b: Evolution of energy with
Appear 6.1.2-c: Evolution of the arrow with
the number of refinements
the number of refinements
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6.1.3 Use
of
MACR_ADAP_MAIL option LIBRE

The first question to regulate during the use of free refinement with HOMARD 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 grid is here linear in order to clearly illustrate the effect of the adaptation of grid, because one saw
previously that the initial grid 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
extract below NOM_CMP_INDICA=' ERREST' in NOM_CMP_INDICA=' NUEST') is activated by
following commands:

# SUBTLETY MACRO_COMMANDE WITH RESPECT TO THE INPUTS
MA [num_calc1] =CO (“MA_ % of % (num_calc1))

# REFINEMENT FREE VIA LOBSTER
# GRID STARTING: MA [num_calc]
# GRID 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 6.1.3-b: Composante

Appear 6.1.3-c: Constraint 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 constraint is weak in a zone
(neutral fiber of the beam in particular) where refinement is less necessary than elsewhere (see the error
K
absolute) the result of standardization rel returns (K)
()
= 100×
random. Indeed,
(K) 2
2
+ H

0, K
it is pointed out that zones with constraint of null standardization will be regarded as having one
error of 100%: if it is necessary to refine in this zone, that will be good (though that will mask the others
zones 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 constraint of standardization.

6.2
Thermoelastic example (simplified bolt)

The following structure is considered:


Y
3
8
4
20
3
10
3
6
3
X
55

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subjected to the following loadings:


GM33
OUTGOING FLOW
2
=-400 W/m

GM36
GM34
2
ECHANGE= (1000 W/m °C, 350°C)
PRES_REP= 0.1N
Y
GM35
X

GM37 2
ECHANGE= (5000 W/m °C, 150°C)
GM39/GM40
DX=DY=0


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 grid [Figure 6.2-a] - one
will note that this grid checks one of our consultings which is to start from a “reasonable” grid - one
carry out a refinement on the relative total error, Cf. the result [Figure 6.2-b]:
# GRID STARTING: MAT [num_calc]
# GRID Of ARRIVES: MAT [num_calc1]
MACR_ADAP_MAIL (
ADAPTATION=_F (
FREE = “RAFF_DERA”,

MAILLAGE_N = MAT [num_calc],
MAILLAGE_NP1 = MAT [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):
# GRID STARTING: MAT [num_calc]
# GRID Of ARRIVES: MAT [num_calc1]
MACR_ADAP_MAIL (
ADAPTATION=_F (
FREE = “RAFF_DERA”,

MAILLAGE_N = MAT [num_calc],
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MAILLAGE_NP1 = MAT [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 grids strongly differ. In the second case of
appear, refinement was indeed directed towards drillings, seats of the conditions of exchanges.


Appear 6.2-a: initial Maillage


Appear 6.2-b: Maillage refined starting from the relative total error
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Appear 6.2-c: Grid 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 step of time has there. According to the consultings given previously, one carries out this calculation
coupled on two different grids: a “thermal” grid linear on which will be based
lumpés elements and a “mechanical” grid quadratic, the passage of the one with the other being carried out
by operator “PROJ_CHAMP”.

More precisely: with each stage of the loop of refinement, one starts by calculating
temperature on the thermal grid:
TEMP [num_calc] =THER_LINEAIRE (
MODELE=MOT [num_calc],
CHAM_MATER=CHMATT [num_calc],
EXCIT= (
_F (CHARGE = CHT [num_calc]),
_F (CHARGE = CLIMT [num_calc],),)
)

then one projects this temperature on the mechanical grid (one created a model beforehand
thermics MOT2 related to the mechanical grid):

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 (CHARGE = CHT [num_calc]),
_F (CHARGE = 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 grids

MACR_ADAP_MAIL (
ADAPTATION=_F (
FREE = “RAFF_DERA”,

MAILLAGE_N = MAT [num_calc],
MAILLAGE_NP1 = MAT [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 (modelled 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 zone 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 step of calculation: the grid is then adapted to each step of calculation
individually. It is then necessary to project the fields of a grid 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 grid.

The first strategy is to be adopted if the zones of refinement evolve/move much, us
in will see an example in following thermal calculation; the second can be adopted if
the zones of refinement evolve/move little, as in this mechanical case where it is a question of following
growth of a plastic zone.
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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 grid 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 constraints 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: Lieu of postprocessing
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Appear 6.3.2-b: Profil of constraint

One will find on the figures [Figure 6.3.2-c] and [Figure 6.3.2-d] the initial grid and the grid 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
Grid 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 grid
Appear 6.3.2-d: Grid 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 zone 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 grid during the transient regularly. In practice, one subdivides
the list of moments in blocks, inside these blocks of moments of calculation the grid 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, a calculation is begun (thus not the “reuse one”)

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 grid of the block of moment (i.e. the last grid of the block of moment
precedent), one again did not create grid (one thus did not carry out a 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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Lastly, if it is about a mending of meshes, one will seek the initial temperature in a 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 grid:

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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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 a CHAM_NO (called “CT here”) in order to use this CHAM_NO as temperature
initial on the new grid:

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 grid:

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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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
grid. As one will be able to note it on the grids initial and adapted (with the last step of time),
Cf [Figure 6.3.3-a] ­ [Figure 6.3.3-b], the grid did not change in the vicinity close to this line of
examination: the improvement of the calculated temperature comes from the zones that one refined by
elsewhere. It will be also noticed that the refined grid is not very intuitive: it is there too about one of
interest of the automatic adaptation of grid.
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Appear 6.3.3-a: initial Maillage
Appear 6.3.3-b: Maillage refined in the last
no calculating time

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Appear 6.3.3-c: Profile of temperature
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Intentionally white left page.
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U2.08 booklet: Advanced function and control of calculations
HT-66/03/002/A

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