Code_Aster
®
Version
8.1
Titrate:
Operator
THER_NON_LINE
Date:
23/06/05
Author (S):
C. DURAND
Key
:
U4.54.02-G1
Page:
1/12
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: U4.54.02
Operator
THER_NON_LINE
1 Goal
To calculate the thermal response with nonlinearities of behaviors and boundary conditions.
The equation of heat is solved in evolutionary mode (except if no list of moment is provided, only
the stationary regime is then calculated). Nonthe linearities come is behavior
(characteristics of material depend on the temperature), that is to say boundary conditions
(radiation in infinite medium, nonlinear flow). A formulation in enthalpy was selected in order to
to more easily take into account the phase shifts of material.
Evolutionary 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 stationary calculation.
This operator also allows to solve the problems of drying (nonlinear) while solving
the equation of the heat where the water C concentration is comparable at a temperature, for
resolution. Thermal conductivity is in this case the coefficient of dissemination, nonlinear out of C and
function, possibly, of a temperature calculated as a preliminary.
To modelize the hydration of the concrete, the operator also allows to add a term function source
variable of hydration to the equation of heat. This term is then given by an equation
of evolution where the temperature intervenes.
The concept produced by the operator
THER_NON_LINE
is of type
evol_ther
as for an analysis
linear by
THER_LINEAIRE
[U4.54.01].
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.
Code_Aster
®
Version
8.1
Titrate:
Operator
THER_NON_LINE
Date:
23/06/05
Author (S):
C. DURAND
Key
:
U4.54.02-G1
Page:
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Instruction manual
U4.5- booklet: Methods of resolution
HT-66/05/004/A
2 Syntax
temper
[evol_ther]
=
THER_NON_LINE
(
reuse
= temper,
MODEL
=
Mo,
[model]
CHAM_MATER
=
chmat,
[cham_mater]
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]
),
SENSITIVITY =_F (
.
.
.
to see
[U4.50.02]
.
.
.
),
INCREMENT =_F (
LIST_INST
=
litps,
[listr8]
NUME_INIT
=/0,
/
nuini,
[I]
NUME_FIN
=
nufin,
[I]
),
COMP_THER_NL =_F (
RELATION
=
/
“THER_NL”,
[DEFECT]
/
“THER_HYDR”, [txm]
/
“SECH_GRANGER”,
[txm]
/
“SECH_MENSI”,
[txm]
/
“SECH_BAZANT”,
[txm]
/
“SECH_NAPPE”,
[txm]
/
ALL =
“YES”,
[txm]
/ |
GROUP_MA = l_grmail,
[l_gr_ma]
|
NET
=
l_maille,
[l_ma]
),
EVOL_THER_SECH =
resuther,
[evol_ther]
Code_Aster
®
Version
8.1
Titrate:
Operator
THER_NON_LINE
Date:
23/06/05
Author (S):
C. DURAND
Key
:
U4.54.02-G1
Page:
3/12
Instruction manual
U4.5- booklet: Methods of resolution
HT-66/05/004/A
NEWTON =_F (
REAC_ITER
=/0,
[DEFECT]
/it,
[I]
RESI_LINE_RELA=/1.E-3, [DEFECT]
/reslin, [R]
ITER_LINE_MAXI=/0,
[DEFECT]
/iterl,
[R]
),
CONVERGENCE=_F (
RESI_GLOB_RELA=/1.E-6, [DEFECT]
/testr,
[R]
RESI_GLOB_MAXI=/testl, [R]
ITER_GLOB_MAXI=
/10, [DEFECT]
/iterl,
[R]
),
PARM_THETA
=
/
theta,
[R]
/0.57,
[DEFECT]
SOLVEUR =_F ([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]
),
OPTION
=
|
“FLUX_ELGA_TEMP”,
[l_Kn]
|
“FLUX_ELNO_TEMP”,
TITRATE
= title,
[l_Kn]
);
Code_Aster
®
Version
8.1
Titrate:
Operator
THER_NON_LINE
Date:
23/06/05
Author (S):
C. DURAND
Key
:
U4.54.02-G1
Page:
4/12
Instruction manual
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
Key word
EXCIT
EXCIT
=
Key word factor allowing to define several loadings. For each occurrence of the key word
factor, one defines a load possibly multiplied by a function of time.
3.3.1 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
.
3.3.2 Operand
FONC_MULT
FONC_MULT = fonc
Multiplicative coefficient function of time (concept of the type
function
) applied to
charge.
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_
,
RADIATION
or
FLUNL
.
3.4 Word
key
TEMP_INIT
TEMP_INIT = litps
Allows to define the initial field from which evolutionary calculation is carried out. The initial field is
affected of the sequence number 0 and the initial moment takes as value the first reality of the list
from moment
litps
.
Note:
If the key word
TEMP_INIT
misses, one carries out only stationary calculation at the moment
defined under the key word
INCREMENT
.
Code_Aster
®
Version
8.1
Titrate:
Operator
THER_NON_LINE
Date:
23/06/05
Author (S):
C. DURAND
Key
:
U4.54.02-G1
Page:
5/12
Instruction manual
U4.5- booklet: Methods of resolution
HT-66/05/004/A
3.4.1 Operand
STATIONARY
/
STATIONARY
=
“YES”
The initial value is then the result of a preliminary stationary calculation. This calculation takes
in account boundary conditions defined under the key word
CHARGE
.
3.4.2 Operand
VALE
/
VALE
=
tinit
The initial value of temperature is taken constant on all the structure.
3.4.3 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]).
3.4.4 Operand
EVOL_THER
/
EVOL_THER = temp
The initial value is extracted from a structure of data of the type
evol_ther
.
3.4.5 Operand
NUME_INIT
NUME_INIT = nuini_evol
Sequence number of the field to be extracted from this structure of data.
The initial field is stored in the structure of data result
temper
under
sequence number 0.
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
.
3.5 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.
3.6 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
a stationary calculation is carried out.
Code_Aster
®
Version
8.1
Titrate:
Operator
THER_NON_LINE
Date:
23/06/05
Author (S):
C. DURAND
Key
:
U4.54.02-G1
Page:
6/12
Instruction manual
U4.5- booklet: Methods of resolution
HT-66/05/004/A
3.6.1 Operand
LIST_INST
LIST_INST = litps
List moments produced by
DEFI_LIST_REEL
[U4.34.01].
3.6.2 Operand
NUME_INIT
NUME_INIT =
/0
/
nuini
Index of the moment of starting calculation in the list
litps
.
If
NUME_INIT
misses and if
evol_ther
is present under
TEMP_INIT,
then
nuini = nuini_evol
.
3.6.3 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
number of moment. Thus the first pitch of time is defined between the moment
agent with
nuini
and that corresponding to
nuini + 1
. Calculation, stationary,
when it is asked, is made at the moment corresponding to
nuini
.
3.7 Word
key
COMP_THER_NL
COMP_THER_NL
=
The resolution of drying was added in Code_Aster because of analogy of the equations of
the thermics and of drying. That supposes to assimilate the variable of calculation of drying,
water concentration, with a variable of the type
“TEMP”
during the resolution.
By defect, the resolution carried out will be nonlinear thermics. This key word factor allows
thus to distinguish the resolution of drying from thermics. Moreover, the equation of drying is
characterized by a coefficient of dissemination which can be expressed in various forms. This key word
factor also makes it possible to choose one of the equations of the drying, defined by the expression of sound
coefficient of dissemination, available in Aster. To carry out a nonlinear calculation of thermics,
this key word becomes optional, and the concept of behavior is transparent for the user.
Note:
If the key word
COMP_THER_NL
misses, one carries out a nonlinear calculation of thermics
“standard”.
3.7.1 Operand
RELATION
RELATION: /
“THER_NL”
[DEFECT]
/
“THER_HYDR”
/
“SECH_GRANGER”
/
“SECH_MENSI”
/
“SECH_BAZANT”
/
“SECH_NAPPE”
The syntax and the processing of this key word are similar to the use of the key words
COMP_INCR
and
COMP_ELAS
of the operator
STAT_NON_LINE
.
/
“THER_NL”
Standard nonlinear thermal resolution.
Supported modelings:
·
continuous mediums 3D:
3D
·
continuous mediums 2D:
2D,
AXIS
Code_Aster
®
Version
8.1
Titrate:
Operator
THER_NON_LINE
Date:
23/06/05
Author (S):
C. DURAND
Key
:
U4.54.02-G1
Page:
7/12
Instruction manual
U4.5- booklet: Methods of resolution
HT-66/05/004/A
/
“THER_HYDR”
Resolution of the equation of heat with an additional source term:
Q &
Q
is the heat of hydration, presumedly constant. The variable of hydration
is
solution of the nonlinear law of evolution, solved simultaneously with the problem of thermics:
&
()
=
-
With
E
E RT
One will refer to the documentation of the operator
DEFI_MATERIAU
for the significance of
various parameters.
Supported modelings:
·
continuous mediums 3D:
3D
·
continuous mediums 2D:
2D,
AXIS
/
“SECH_GRANGER”
Resolution of the drying characterized by the equation
()
[
]
C
T
Div D C T
C
-
=
,
0
It is the equation of nonlinear heat where the variable of drying
C
the role holds of
temperature. The choice of the relation of behavior makes it possible to define the coefficient of
dissemination
()
D C T
,
according to various usual forms of the literature. The formulation of
Granger of the coefficient of dissemination is given by the expression:
D C T
With
BC T
T
Q
R T
T
S
(,)
exp (
)
exp
=
-
-
0
0
1
1
One will refer to the documentation of the operator
DEFI_MATERIAU
for the significance of
various parameters. In the case of the use of this law
SECH_GRANGER
, it is
necessary to ensure itself of coherence enters the material used and the law of behavior:
i.e. that the key word
SECH_GRANGER
indeed was well informed in
DEFI_MATERIAU
for
the material used.
Supported modelings:
·
continuous mediums 3D:
3D
·
continuous mediums 2D:
2D,
AXIS
As the resolution of drying is carried out by an operator of thermics, them
supported modelings are thermal modelings, but which do not have whereas one
conceptual value of a geometrical nature.
/
“SECH_MENSI”
Resolution of the drying characterized by the law of MENSI.
In the case of the use of this law
SECH_MENSI
, it is necessary to be ensured of
coherence enters the material used and the law of behavior: i.e. that the key word
SECH_MENSI
indeed was well informed in
DEFI_MATERIAU
for material used.
Supported modelings: analog with
SECH_GRANGER
.
/
“SECH_BAZANT”
Resolution of the drying characterized by the law of BAZANT.
In the case of the use of this law
SECH_BAZANT
, it is necessary to be ensured of
coherence enters the material used and the law of behavior: i.e. that the key word
SECH_BAZANT
indeed was well informed in
DEFI_MATERIAU
for material used.
Supported modelings: analog with
SECH_GRANGER
.
Code_Aster
®
Version
8.1
Titrate:
Operator
THER_NON_LINE
Date:
23/06/05
Author (S):
C. DURAND
Key
:
U4.54.02-G1
Page:
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Instruction manual
U4.5- booklet: Methods of resolution
HT-66/05/004/A
/
“SECH_NAPPE”
Resolution of drying with a coefficient of dissemination defined by a tablecloth Aster.
In the case of the use of this law
SECH_NAPPE
, it is necessary to be ensured of
coherence enters the material used and the law of behavior: i.e. that the key word
SECH_NAPPE
indeed was well informed in
DEFI_MATERIAU
for material used.
Supported modelings: analog with
SECH_GRANGER
.
3.7.2 Operands
ALL/GROUP_MA/MESH
/ALL = “YES”
/
GROUP_MA = l_grmail
/
NET =
l_maille
Specify the meshs to which the relation of behavior is applied. In way
analog with mechanics, one can use several different laws of drying, applied
with groups of complementary meshs. On the other hand, thermal cannot be it
mixed with drying. The behavior
“THER_NL”
is necessarily applied to all
mesh, option
ALL: “YES”
, default option, which is in fact, in the general case,
transparent for the user.
3.8 Operand
EVOL_THER_SECH
EVOL_THER_SECH=
resuther
This operand is specific to the resolution of drying. Drying is solved after a calculation
preliminary thermics in the general case, (calculation not coupled but chained thermal/drying), it
thermal field intervening like auxiliary variable, allowing to calculate the coefficient of
diffusion of certain laws. It is an input datum of the calculation of the drying, which must be one
structure of data of the type
evol_ther
. This key word is obligatory only for the laws
“SECH_GRANGER”
and
“SECH_NAPPE”
, whose coefficient of dissemination depends on the temperature.
The structure of data of here well informed thermal evolution will have been obtained by an execution
the preceding one of an operator of thermics, linear or not.
3.9 Word
key
NEWTON
NEWTON =
Specify the characteristics of the method of resolution of the nonlinear problem (method of
NEWTON-RAPHSON).
3.9.1 Operand
REAC_ITER
REAC_ITER
=/0 [DEFECT]
/it
The matrix used for the total iterations of the method is the tangent matrix which
is revalued at the beginning of each increment of time and all them
it
iterations of
NEWTON for an increment of time given (precisely to the iterations of number
it
,
2it
,
3it
…). Thus with the first iteration of NEWTON, one does not reassemble the matrix
tangent that if
it
1 is worth: if not one keeps the matrix used in the phase of
prediction. By convention if
it
the 0 matrix is worth is not revalued during all the pitch
time.
Code_Aster
®
Version
8.1
Titrate:
Operator
THER_NON_LINE
Date:
23/06/05
Author (S):
C. DURAND
Key
:
U4.54.02-G1
Page:
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Instruction manual
U4.5- booklet: Methods of resolution
HT-66/05/004/A
3.9.2 Operand
RESI_LINE_RELA/ITER_LINE_MAXI
RESI_LINE_RELA =/1.E-3
[DEFECT]
/reslin
ITER_LINE_MAXI
=
/0 [DEFECT]
/itlin
In fact the parameters of linear search make it possible to ensure the best
convergence of the method of NEWTON (cf [R5.03.01] for more details). One gives
the maximum iteration count
itelin
to carry out (the default value 0 indicates that
one does not make linear search) and the precision
reslin
to reach to realize
convergence of linear search.
Note:
It is not necessary to specify a precision very nor an iteration count
raised, practice showing that 2 or 3 iterations of linear search are
sufficient. One can thus be satisfied to ask for 3 iterations with
precision by defect.
3.10 Word
key
CONVERGENCE
CONVERGENCE:
Allows to define the values associated with the criteria with convergence:
If none of the two operands following is present, then all occurs like if:
RESI_GLOB_RELA = 1.E-6
.
3.10.1 Operand
RESI_GLOB_RELA
RESI_GLOB_RELA =/1.e-6
/testr
The algorithm continues the external iterations as long as the relative residue is higher than
testr
.
()
()
F
S
in
I
Nb ddl
I
I
Nb ddl
2
1
1 2
2
1
1 2
=…
=…
>
,
/
,
/
testr
where
F
I
indicate the residue and
S
I
the thermal loading, the index
N
indicate N
ième
iteration.
3.10.2 Operand
RESI_GLOB_MAXI
RESI_GLOB_MAXI =
/
1.e-3
/testl
The algorithm continues the external iterations as long as the absolute residue is higher than
testl
.
I
Nb ddl
in
F
=…
>
1,
max
testl
where
F
I
indicate the residue, the index
N
indicate N
ième
iteration.
3.10.3 Operand
ITER_GLOB_MAXI
ITER_GLOB_MAXI =/10
/iterl
The algorithm continues the iterations as long as their number is lower than
iterl
.
Code_Aster
®
Version
8.1
Titrate:
Operator
THER_NON_LINE
Date:
23/06/05
Author (S):
C. DURAND
Key
:
U4.54.02-G1
Page:
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Instruction manual
U4.5- booklet: Methods of resolution
HT-66/05/004/A
3.11 Operand
PARM_THETA
PARM_THETA = 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
corresponds 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].
3.12 Word
key
SOLVEUR
SOLVEUR =
This key word factor is optional: it makes it possible to choose another solvor of resolution of system.
This operand is common to the whole of the total controls [U4.50.01].
3.13 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 for tocker 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.
3.13.1 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
.
3.13.2 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.
3.13.3 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].
3.14 Operand
OPTION
OPTION = “FLUX_ELGA_TEMP”
This option carries out the calculation of the heat transfer rate at the points of integration from
temperature.
OPTION = “FLUX_ELNO_TEMP”
This option carries out the calculation of the heat transfer rate to the nodes starting from the temperature. Calculation
precondition of
“FLUX_ELGA_TEMP”
is not obligatory.
3.15 Operand
TITRATE
TITRATE
=
titrate
Titrate that one wants to give to the result stored in
temper
, structure of data of the type
evol_ther
[U4.03.01].
Code_Aster
®
Version
8.1
Titrate:
Operator
THER_NON_LINE
Date:
23/06/05
Author (S):
C. DURAND
Key
:
U4.54.02-G1
Page:
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Instruction manual
U4.5- booklet: Methods of resolution
HT-66/05/004/A
4 Modeling
The problems of nonlinear thermics can be dealt with with models using the elements
stop 3D, 2D or AXIS described in the documents [U3.22.01], [U3.23.01] and [U3.23.02] and [U3.24.01].
5 Example
One defined below the main controls used to carry out a calculation of thermics
non-linear transient. The example indicates how to continue calculation by enriching the concept
result and how to specify the “initial” field.
LR8 = DEFI_LIST_REEL (BEGINNING = 0.D0,
INTERVAL =_F (
JUSQU_A=5.e-3, NOMBRE= 10),
INTERVAL =_F (
JUSQU_A=5.e-2, NOMBRE= 9),
INTERVAL =_F (
JUSQU_A=4.e-0, NOMBRE= 79),
INTERVAL =_F (
JUSQU_A=6.e-0, NOMBRE= 20),
)
conduc =
DEFI_FONCTION (
NOM_PARA
=
“TEMP”,
VALE =_F (
0.0
,
210.0,
660.0, 210.0,
660.01,
95.0,
1200.00,
95.0
)
PROL_DROIT
=
“LINEAR”,
PROL_GAUCHE =
“LINEAR”,
)
enthal =
DEFI_FONCTION
(
NOM_PARA
=
“TEMP”,
VALE =_F (
0.0
,
0.0,
660.0
,
1.980E9,
660.01,
3.060E9,
1200.00,
4.451E9
)
PROL_DROIT
=
“LINEAR”,
PROL_GAUCHE =
“LINEAR”,
)
aluminum = DEFI_MATERIAU
(THER_NL =_F (LAMBDA
= conduc,
BETA =
enthal
)
)
…
temple
= THER_NON_LINE (MODELE=moth, CHAM_MATER=chmat,
TEMP_INIT
=_F (VALE
=
20.0
),
INCREMENT
=_F (LIST_INST
=
lr8),
EXCIT
=_F (LOAD
=
chth
),
CONVERGENCE =_F (RESI_GLOB_RELA
=1.E-6,
ITER_GLOB_MAXI
=10
),
)
…
temple = THER_NON_LINE
(reuse = temple,
MODELE=moth
,
CHAM_MATER=chmat,
TEMP_INIT
=_F (EVOL_THER
=
temple,
NUME_INIT
=
20),
INCREMENT
=_F (LIST_INST
=
lr8),
EXCIT
=_F (LOAD
=
chth
),
CONVERGENCE =_F (RESI_GLOB_RELA
=
1.E-6,
ITER_GLOB_MAXI=
10
)
)
…
END ();
Code_Aster
®
Version
8.1
Titrate:
Operator
THER_NON_LINE
Date:
23/06/05
Author (S):
C. DURAND
Key
:
U4.54.02-G1
Page:
12/12
Instruction manual
U4.5- booklet: Methods of resolution
HT-66/05/004/A
Intentionally white left page.