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Code_Aster
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Version
8.1
Titrate:
Operator
THER_LINEAIRE
Date:
23/06/05
Author (S):
C. DURAND
Key
:
U4.54.01-I1
Page
:
1/8
Instruction manual
U4.5- booklet: Methods of resolution
HT-66/05/004/A
Organization (S):
EDF-R & D/AMA














Instruction manual
U4.5- booklet:Methods of resolution
Document: U4.54.01



Operator
THER_LINEAIRE


1 Goal
To solve a linear problem of thermics in stationary regime or evolutionary.
The thermal loading is defined by the key word
CHARGE
.
The temporal discretization of an evolutionary calculation is provided by the list of moments defined under the key word
LIST_INST
. This calculation can be initialized, at the first moment, in three different ways (key word
TEMP_INIT
):
·
by a constant temperature,
·
by a field of temperature, definite, or extracted as a preliminary from a preceding calculation,
·
by a preliminary stationary calculation.
The concept produced by this operator is of type
evol_ther
.
When a calculation of sensitivity of the result compared to a parameter is required, there is production
of as many structures of data of the type
evol_ther
that necessary parameters.
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Code_Aster
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Version
8.1
Titrate:
Operator
THER_LINEAIRE
Date:
23/06/05
Author (S):
C. DURAND
Key
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U4.54.01-I1
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Instruction manual
U4.5- booklet: Methods of resolution
HT-66/05/004/A
2 Syntax
temper
[evol_ther]
=
THER_LINEAIRE
(
reuse
=
temper,
MODEL
=
Mo,
[model]
CHAM_MATER
=
chmat,
[cham_mater]
CARA_ELEM
=
carac,
[cara_elem]
EXCIT
=
_F (
CHARGE
=
tank,
[load]
FONC_MULT
=
fonc,
[function]
),
TEMP_INIT =_F (
/STATIONARY
=
“YES”, [DEFECT]
/VALE
= tinit,
[R]
/
CHAM_NO =
tinit,
[cham_no_TEMP_R]
/
EVOL_THER = temp,
[evol_ther]
NUME_INIT = nuini_evol, [I]
),
SENSIBILITE=_F (
.
.
.
to see
[U4.50.02]
.
.
.
),
SENS_INIT =_F (
/STATIONARY
=
“YES”, [DEFECT]
/
EVOL_THER = temp,
[evol_ther]
NUME_INIT = nuini,
[I]
),
INCREMENT =_F (
LIST_INST
=
litps,
[listr8]
NUME_INIT
=/0,
/
nuini,
[I]
NUME_FIN
=
nufin,
[I]
),
PARM_THETA
=
/theta,
[R]
/
0.57,
[DEFECT]
SOLVEUR
=_F (
… to see [U4.50.01]…),
FILING
=_F
(/
LIST_ARCH
= l_arch
, [listis]
/
PAS_ARCH = ipas, [I]
/
LIST_INST
= l_inst
, [listr8]
/
INST = inst, [R]
PRECISION
=/
10.- 3, [DEFECT]
/
prec
[R]
CRITERION =/
“RELATIVE”,
[DEFECT]
/
“ABSOLUTE”,
CHAM_EXCLU
= l_cham
, [l_Kn]
),
TITRATE
=
titrate,
[l_Kn]
)
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Code_Aster
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Version
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Titrate:
Operator
THER_LINEAIRE
Date:
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Key
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U4.54.01-I1
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U4.5- booklet: Methods of resolution
HT-66/05/004/A
3 Operands
3.1 Operand
MODEL
MODEL = Mo
Name of the model whose elements are the subject of thermal calculation.
3.2 Operand
CHAM_MATER
CHAM_MATER = chmat
Name of the affected material field on the model.
3.3 Operand
CARA_ELEM
CARA_ELEM = carac
The concept
carac
contains the characteristics of the elements of thermal hull, if they exist
in the model.
3.4 Word
key
EXCIT
EXCIT
=
Operand allowing to define several loadings. For each occurrence of the key word
factor, one defines a load possibly multiplied by a function of time.
3.4.1 Operand
CHARGE
CHARGE = tank
Concept of the type
charge
product by
AFFE_CHAR_THER
or by
AFFE_CHAR_THER_F
[U4.44.02].
Important remark:
For each occurrence of the key word factor
EXCIT
various concepts
tank
used
must be built on the same model
Mo
.
3.4.2 Operand
FONC_MULT
FONC_MULT = fonc
Multiplicative coefficient function of time (concept of the type
function
) applied to the load.
Important remark:
The concomitant use of
FONC_MULT
with a load containing of
thermal loadings depending on the temperature is prohibited; i.e. for
loadings of the type
ECHANGE_ *
.
3.5 Word
key
TEMP_INIT
TEMP_INIT
=
Allows to define the initial field from which evolutionary calculation is carried out.
Note:
If the key word
TEMP_INIT
misses, one carries out only stationary calculation with
the moment defined under the key word
INCREMENT
.
The initial field is stored in the structure of data result
evol_ther
under
sequence number 0.
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Titrate:
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THER_LINEAIRE
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U4.5- booklet: Methods of resolution
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3.5.1 Operand
STATIONARY
/
STATIONARY
=
“YES”
The initial value of the field of temperature is then the result of a stationary calculation
precondition.
3.5.2 Operand
VALE
/
VALE
=
tinit
The initial value of temperature is taken constant on all the structure.
3.5.3 Operand
CHAM_NO
/
CHAM_NO
=
tinit
The initial value is defined by one
cham_no_TEMP_R
(result of the operators
AFFE_CHAM_NO
[U4.44.11] or
RECU_CHAMP
[U4.71.01]).
3.5.4 Operand
EVOL_THER
/
EVOL_THER = temp
The initial value is extracted from a structure of data of the type
evol_ther
.
3.5.5 Operand
NUME_INIT
NUME_INIT = nuini_evol
Sequence number of the field to be extracted from this structure of data.
Note:
Attention, it acts of the sequence number in the structure of data read in recovery by
the key word
EVOL_THER
precedent. If this structure of data were calculated with
a list of moments different from that used under the key word factor
INCREMENT
of
the current resolution, it is imperative to inform
NUME_INIT
under
INCREMENT
,
the same value of sequence number corresponding to physical moments
different. If the two lists of moments are identical, one can
to exempt to inform the same one twice
NUME_INIT
, under
ETAT_INIT
and under
INCREMENT
.
3.6 Word
key
SENSITIVITY
SENSITIVITY = sensitive parameter list
Activate the calculation of derived from the field of temperature compared to a significant parameter
problem.
The document [U4.50.01] specifies the operation of the key word.
3.7 Word
key
SENS_INIT
SENS_INIT
=
Allows to define the initial field from which the evolutionary calculation of derived from
temperature is carried out, for a transitory calculation.
Note:
If the key word
SENS_INIT
misses, initialization is made by a field with the nodes
no one.
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Titrate:
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THER_LINEAIRE
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3.7.1 Operand
STATIONARY
/
STATIONARY
=
“YES”
The initial value is that of a preliminary stationary calculation. That is not possible that if it
even mode of initialization is retained for the calculation of the temperature.
3.7.2 Operand
EVOL_THER
/
EVOL_THER = temp
The initial value is extracted from a structure of data of the type
evol_ther
.
3.7.3 Operand
NUME_INIT
NUME_INIT = nuini_evol
Sequence number of the field to be extracted from this structure of indicated data.
3.8 Word
key
INCREMENT
INCREMENT =
Allows to define the moments of calculation which determine the intervals of time taken to integrate
the differential equation.
Note:
If the key word
INCREMENT
misses, one creates a list of moments reduced to the only reality
0 and one carry out a stationary calculation.
3.8.1 Operand
LIST_INST
LIST_INST = litps
List moments, produced by
DEFI_LIST_REEL
[U4.34.01].
3.8.2 Operand
NUME_INIT
NUME_INIT =
/0
/nuini
Index of the moment of starting calculation in the list
litps
.
3.8.3 Operand
NUME_FIN
NUME_FIN = nufin
Index of the moment of final calculation in the list
litps
.
The moments of calculation are those defined in the concept
litps
taken between
nuini
and it
nufin
who are numbers of moment. Thus the first pitch of time is defined between the moment
agent with
nuini
and that corresponding to
nuini + 1
. Stationary calculation, when it
is asked, is made at the moment corresponding to
nuini
.
If
NUME_INIT
misses and if
temp
is present under
TEMP_INIT
, then
nuini = nuini_evol
.
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Titrate:
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THER_LINEAIRE
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3.9 Operand
PARM_THETA
PARM_THETA
=
The argument
theta
is the parameter of the théta-method applied to the evolutionary problem. It must
to lie between 0 (explicit method) and 1 (completely implicit method). In the absence, word
key, the value used is
theta=0.57
, a little higher than
theta=0.5
corresponding to the diagram
of Crank-Nicholson. The angle of attack of the choice of
theta
on the stability of the method is detailed
in [R5.02.02].

3.10 Word
key
SOLVEUR
SOLVEUR =
This key word factor is optional: it makes it possible to define the method of resolution of the systems
linear.
This operand is common to the whole of the total controls [U4.50.01].

3.11 Word
key
FILING
FILING
=
This key word is optional: by defect, the whole of the computed fields for all the calculated pitches
is filed in the concept
result
resulting from the control. It is used to store certain numbers
of command in a structure of data
result
and/or to exclude from storage certain fields.
Note:
In the event of stop of calculation for lack of time CPU, pitches of time previously
calculated are backed up in the base.
3.11.1 Operand
LIST_ARCH
Concept of the type lists of entirety created by the control
DEFI_LIST_ENTI
[U4.34.02] describing the list
sequence numbers having to be stored in the structure of data
result
.
3.11.2 Operand
PAS_ARCH
Whole value giving the value of pitch of filing: one will store the multiple sequence numbers of
value
ipas
as well as the last actually calculated sequence number.
3.11.3 Operand
CHAM_EXCLU
List texts indicating the fields excluded from filing. The list of the possible fields is
described in the documents on the concepts
result
[U5.01].
3.12 Operand
TITRATE
TITRATE
=
titrate
Titrate that one wants to give to the result
temp
stored in the structure of data of the type
evol_ther
[U4.03.01].


4 Modeling
The problems of linear thermics can be dealt with with models using the finite elements
3D, 2D, AXIS or HULL described in the documents [U3.22.01], [U3.23.01], [U3.23.02] and [U3.24.01].
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Code_Aster
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Version
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Titrate:
Operator
THER_LINEAIRE
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Key
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U4.54.01-I1
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Instruction manual
U4.5- booklet: Methods of resolution
HT-66/05/004/A
5 Example
5.1 Calculation
transient
LR8 = DEFI_LIST_REEL (BEGINNING
=
0.E0
,
INTERVAL
= (
_F (JUSQU_A = 2.E-4, A NUMBER
= 2),
_F (JUSQU_A = 1.E-3, A NUMBER
= 10
),
_F (JUSQU_A = 1.E-2, A NUMBER
= 9),
_F (JUSQU_A = 1.E-1, A NUMBER
= 9),
_F (JUSQU_A = 1.E+0, A NUMBER
= 9),
_F (JUSQU_A = 2.0
, A NUMBER
= 10
),)
)
temple = THER_LINEAIRE
(MODEL
= moth,
CHAM_MATER = chmat,
EXCIT
= _F (LOAD
=
chth),
TEMP_INIT
=
_F (
STATIONARY = “yes”),
INCREMENT
=
_F (
LIST_INST
= lr8,
NUME_FIN
= 30)
)
temple = THER_LINEAIRE
(reuse = temple,
MODEL
=
moth,
CHAM_MATER = chmat,
EXCIT
= _F (LOAD
=
chth),
TEMP_INIT
=
_F (
EVOL_THER
= temple
NUME_INIT
= 30),
INCREMENT
=
_F (
LIST_INST
= lr8),
)
The first call to the control
THER_LINEAIRE
allows to carry out a stationary calculation at the moment
0. and to connect an evolutionary calculation until the moment 0.1s (31 moments of calculation are 30 calculations
of evolution).
The second call makes it possible to enrich the concept
temple
precedent, evolutionary calculation is continued to leave
from the 31
ième
moment of calculation.
5.2
Sensitivity to an imposed temperature
your
= DEFI_PARA_SENSI (VALE = 70
)
Tb
= DEFI_PARA_SENSI (VALE = 30
)
Ca
= AFFE_CHAR_THER_F
(MODEL
= moth,
TEMP_IMPO
= (
_F (
GROUP_MA = “bord_sup”,
TEMP
= your),
_F (GROUP_MA = “bord_inf”,
TEMP
= Tb))
)
temple = THER_LINEAIRE
(MODEL
= moth,
CHAM_MATER = chmat,
EXCIT
=_F (LOAD
=
chth),
SENSIBILITE=
(
your
,
Tb
),
)
This calculation will produce the structure of data
temple
, of type
evol_ther
, containing the field of
temperature under the name
TEMP
. It will produce also two other structures of the type
evol_ther
.
first will contain, under the name of field
TEMP
, the field of derived from the temperature by
report/ratio with the parameter
your
. The second will contain the derivative compared to the parameter
Tb
. The name of
these structures is created automatically by the code and remains unknown to the user. The access to their
contents (impression, test, post_releve…) is done by calling upon the corresponding control with
name of the main structure,
temp
, and the name of the significant parameter concerned,
your
or
Tb
.
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Code_Aster
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Titrate:
Operator
THER_LINEAIRE
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Instruction manual
U4.5- booklet: Methods of resolution
HT-66/05/004/A
6 Remark
The control
CALC_ELEM
[U4.81.01] allows to calculate the heat transfer rates, at the points of integration
or with the nodes, the field with the nodes of temperature thus obtained by
THER_LINEAIRE
.