Code_Aster ®
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Note of use of model THM


Date:
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:
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Organization (S): EDF-R & D/AMA
Handbook of Utilization
U2.04 booklet: Nonlinear mechanics
Document: U2.04.05

Note of use of model THM

Summary:

One details the procedure to be followed here for the realization of a calculation THM.
Handbook of Utilization
U2.04 booklet: Nonlinear mechanics
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Note of use of model THM


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Count

matters

1 the broad outline ................................................................................................................................. 3
1.1 Context of studies THM ............................................................................................................... 3
1.2 General information ...................................................................................................................................... 3
1.3 Stages of calculations ............................................................................................................................. 4
2 various stages of calculation ............................................................................................................ 4
2.1 Choice of the model .............................................................................................................................. 4
2.2 Definition of the material ...................................................................................................................... 7
2.2.1 Key word factor ELAS ............................................................................................................... 8
2.2.2 Single-ended spanner word COMP_THM ...................................................................................................... 8
2.2.3 Key word factor THM_INIT .................................................................................................... 10
2.2.4 Key word factor THM_LIQU .................................................................................................... 12
2.2.5 Key word factor THM_GAZ ...................................................................................................... 13
2.2.6 Key word factor THM_VAPE_GAZ ........................................................................................... 13
2.2.7 Key word factor THM_AIR_DISS ........................................................................................... 14
2.2.8 Key word factor THM_DIFFU ................................................................................................. 15
2.2.9 Recapitulation of the functions of couplings and their dependence .......................................... 19
2.2.9.1 Key word factor THM_DIFFU ...................................................................................... 20
2.3 Initialization of calculation ..................................................................................................................... 22
2.4 Loadings and boundary conditions .......................................................................................... 25
2.5 Nonlinear calculation ..................................................................................................................... 27
2.6 Postprocessing .......................................................................................................................... 30
2.6.1 Isovaleurs with Gibi ............................................................................................................. 31
2.6.2 Isovaleurs with IDEAS ......................................................................................................... 32
3 Bibliography ........................................................................................................................................ 32
Appendix 1
Generalized constraints and variables intern ........................................................ 33
Appendix 2
Example I of command file .......................................................................... 34
Appendix 3
Example 2 of command files ....................................................................... 37
Appendix 4
Post processing GIBI ................................................................................................. 42
Appendix 5
Additional elements on the boundary conditions in THM .......................... 44
Handbook of Utilization
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Note of use of model THM


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1
The broad outline

1.1
Context of studies THM

First of all, it is advisable to define the quite precise framework of Hydro-Mécaniques Thermo- calculations.
Those have as an exclusive application the study of the porous environments. Knowing that, modelings THM
cover L `evolution mechanical of these mediums and the flows in their center. The latter concern
one or two fluids and is governed by the laws of Darcy (fluid darcéens). The problem of complete THM
draft thus of the flow of or the fluid (S), the mechanics of the skeleton, as well as
thermics: the resolution is entirely coupled (and not chained).

1.2 General

Calculations are based on families of laws of behavior THM for the saturated porous environments
and unsaturated. The mechanics of the porous environments gathers a very exhaustive collection of
physical phenomena concerning with the solids and the fluids. It makes the assumption of a coupling enters
mechanical evolutions of the solids and the fluids, seen like continuous mediums, with
hydraulic evolutions, which regulate the problems of diffusion of fluids within walls or of
volumes, and thermal evolutions. The formulation of hydro-mechanical Thermo- modeling
(THM) in porous environment such as it is made in Code_Aster is detailed in [R7.01.11] and
[R7.01.10]. All the notations employed here thus refer to it. One recalls however some
essential notations thereafter:

Concerning the fluids, one considers (the most complete case) two phases (liquid and gas) and two
components called by convenience water and air. The following indices then are used:

W for liquid water
AD for the dissolved air
have for the dry air
vp for the steam

The thermodynamic variables are:

· pressures of the components: pw (,
X T), pad (,
X T), pvp (,
X T), not (,
X T),
· the temperature of the medium T (X, T).

These various variables are not completely independent. Indeed, if only one is considered
component, thermodynamic balance between its phases imposes a relation between the pressure of
vapor and pressure of the liquid of this component. Finally, there is only one pressure
independent by component, just as there is only one conservation equation of the mass.
The number of independent pressures is thus equal to the number of independent components.
choice of these pressures varies according to laws' of behaviors.

For the case known as saturated (only one component air or water) we chose the pressure of this single
component.
For the case says unsaturated (presence of air and water), we chose like variables
independent:

· total pressure of the gas p
,
X T =p + p,
gz (
) vp have
· capillary pressure p
,
X T = p - p = p - p - p
C (
) gz
lq
gz
W
AD.

We will see the Aster terminology thereafter for these variables.
Handbook of Utilization
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Note of use of model THM


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1.3
Stages of calculations

For the stages necessary to the manufacture of a Aster calculation, independently of the aspects
purely THM, one will refer to the documentation of each command used.
In the whole of this document one will refer to a typical example of file of calculation given in
appendix. In any Aster calculation, several key stages must be carried out:

· Choice of modeling
· Data materials
· Initialization
· Calculation
· Postprocessing

2
Various stages of calculation

2.1
Choice of the model

The choice is done by the use of command AFFE_MODELE as in the example below:

MODELE=AFFE_MODELE (MAILLAGE=MAIL,
AFFE=_F (TOUT=' OUI',
PHENOMENE=' MECANIQUE',
MODELISATION=' AXIS_THH2MD',),);

The digital processing in THM requires a quadratic grid since the elements are of type
P2 in displacement and P1 in pressure and temperature in order to avoid problems of oscillations.
Phenomenon “MECANIQUE” is obligatory whatever the selected type of modeling (with or
without mechanics).
The user must inform here in an obligatory way key word MODELISATION. This key word allows
to define the type of affected element in a type of mesh. Modelings available in THM are them
following:

MODELING Modeling
Phenomena taken into account
geometrical
D_PLAN_HM
plane
Mechanics, hydraulics with an unknown pressure
D_PLAN_HMD
plane
Mechanics, hydraulics with an unknown pressure (lumpé)
D_PLAN_HHM
plane
Mechanics, hydraulics with two unknown pressures
D_PLAN_HHMD
plane
Mechanics, hydraulics with two unknown pressures
(lumpé)
Plane D_PLAN_HH2MD
Mechanics, hydraulics with two unknown pressures and
two components per phase (lumpé)
D_PLAN_THH
plane
Thermics, hydraulics with two unknown pressures
D_PLAN_THHD
plane
Thermics, hydraulics with two unknown pressures
(lumpé)
Plane D_PLAN_THH 2D
Thermics, hydraulics with two unknown pressures and two
components by phase (lumpé)
D_PLAN_THM
plane
Thermics, mechanics, hydraulics with a pressure
unknown factor
D_PLAN_THVD
plane
Thermics, mechanics, hydraulics with two pressures
unknown factors (2 phases: liquid water and vapor) (lumpé)
D_PLAN_THMD
plane
Thermics, mechanics, hydraulics with a pressure
unknown factor (lumpé)
D_PLAN_THHM
plane
Thermics, mechanics, hydraulics with two pressures
unknown factors
Plane D_PLAN_THHMD
Thermics, mechanics, hydraulics with two pressures
unknown factors (lumpé)
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Plane D_PLAN_THH2MD
Thermics, mechanics, hydraulics with two pressures
unknown factors and two components per phase (lumpé)
AXIS_HM
axisymmetric Mécanique,
hydraulics with an unknown pressure
AXIS_HMD
axisymmetric Mécanique,
hydraulics
with an unknown pressure (lumpé)
AXIS_HHM
axisymmetric Mécanique,
hydraulics with two unknown pressures
AXIS_HHMD
axisymmetric Mécanique,
hydraulics with two unknown pressures
(lumpé)
AXIS_HH2MD
axisymmetric Mécanique,
hydraulics
with two unknown pressures and
two components per phase (lumpé)
AXIS_THH
axisymmetric Thermique,
hydraulics
with two unknown pressures
AXIS_THHD
axisymmetric Thermique,
hydraulics with two unknown pressures
(lumpé)
AXIS_THH 2D
axisymmetric
Thermics, hydraulics with two unknown pressures and two
components by phase (lumpé)
AXIS_THM
axisymmetric Thermique,
mechanics, hydraulics with a pressure
unknown factor
AXIS_THMD
axisymmetric Thermique,
mechanics, hydraulics with a pressure
unknown factor (lumpé)
AXIS_THVD
axisymmetric Thermique,
mechanics,
hydraulics with two pressures
unknown factors (2 phases: liquid water and vapor) (lumpé)
AXIS_THHM
axisymmetric Thermique,
mechanics,
hydraulics with two pressures
unknown factors
AXIS_THHMD
axisymmetric Thermique,
mechanics,
hydraulics with two pressures
unknown factors (lumpé)
AXIS_THH2MD
axisymmetric Thermique,
mechanics,
hydraulics with two pressures
unknown factors and two components per phase (lumpé)
3d_HM
3D
Mechanics, hydraulics with an unknown pressure
3d_HMD
3D
Mechanics, hydraulics with an unknown pressure (lumpé)
3d_HHM
3D
Mechanics, hydraulics with two unknown pressures
3d_HHMD
3D
Mechanics, hydraulics with two unknown pressures
(lumpé)
3d_HH2MD
3D
Mechanics, hydraulics with two unknown pressures and
two components per phase (lumpé)
3d_THH
3D
Thermics, hydraulics with two unknown pressures
3d_THHD
3D
Thermics, hydraulics with two unknown pressures
(lumpé)
3d_THH 2D
3D
Thermics, hydraulics with two unknown pressures and two
components by phase (lumpé)
3d_THM
3D
Thermics, mechanics, hydraulics with a pressure
unknown factor
3d_THMD
3D
Thermics, mechanics, hydraulics with a pressure
unknown factor (lumpé)
3d_THVD
3D
Thermics, mechanics, hydraulics with two pressures
unknown factors (2 phases: liquid water and vapor) (lumpé)
3d_THHM
3D
Thermics, mechanics, hydraulics with two pressures
unknown factors
3d_THHMD
3D
Thermics, mechanics, hydraulics with two pressures
unknown factors (lumpé)
3d_THH2MD
3D
Thermics, mechanics, hydraulics with two pressures
unknown factors and two components per phase (lumpé)

The principal unknown factors which are also the values of the degrees of freedom, are noted in the case of
the most complete modeling (thermal, mechanical, hydraulic 3D with two pressures
unknown factors).
Handbook of Utilization
U2.04 booklet: Nonlinear mechanics
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Code_Aster ®
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Note of use of model THM


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ux



uy



U
{U} ddl Z

=
ddl
PRE1


ddl
PRE 2

ddl

T


The contents of PRE1 and PRE2 depend on the selected coupling and will be clarified in section 2.2.3.
According to modeling chosen, only some of these degrees of freedom exist. The table above
summarize the degrees of freedom used for each modeling

MODELISATION
U
U
U
ddl
X
y
Z
1
PRE

ddl
PRE2
ddl
T

D_PLAN_HM
X X X
D_PLAN_HMD
X X X
D_PLAN_HHM
X X X X
D_PLAN_HHMD
X X X X
D_PLAN_HH2MD
X X X X
D_PLAN_THH
X
X
X
D_PLAN_THHD
X
X
X
D_PLAN_THH 2D
X
X
X
D_PLAN_THM
X X X X
D_PLAN_THMD
X X X X
D_PLAN_THVD



X
X
X
D_PLAN_THHM
X X X X X
D_PLAN_THHMD
X X X X X
D_PLAN_THH2MD
X X X X X
AXIS_HM
X X X
AXIS_HMD
X X X
AXIS_HHM
X X X X
AXIS_HHMD
X X X X
AXIS_HH2MD
X X X X
AXIS_THH
X
X
X
AXIS_THHD
X
X
X
AXIS_THH 2D
X
X
X
AXIS_THM
X X X X
AXIS_THMD
X X X X
AXIS_THVD



X
X
X
AXIS_THHM
X X X X X
AXIS_THHMD
X X X X X
AXIS_THH2MD
X X X X X
3d_HM
X X X X
3d_HMD
X X X X
3d_HHM
X X X X X
3d_HHMD
X X X X X
3d_HH2MD
X X X X X
3d_THH
X
X
X
3d_THHD
X
X
X
3d_THH 2D
X
X
X
3d_THM
X X X X X
3d_THMD
X X X X X
3d_THVD



X
X
X
3d_THHM
X X X X X X
Handbook of Utilization
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MODELISATION
U
U
U
ddl
X
y
Z
1
PRE

ddl
PRE2
ddl
T

3d_THHMD
X X X X X X
3d_THH2MD
X X X X X X

The generalized constraints and the variables intern all are indicated in [§Annexe 1].
notations used are those defined in [R7.01.11].

Notice concerning the digital processing (key word ending in D):

Modelings ending in the letter D indicate that one makes an allowing processing
of diagonaliser (“lumper”) the matrix of mass in order to avoid the oscillations. For that them
points of integration are taken at the tops of the elements. One advises highly with the user
systematically to choose this type of modeling.

2.2
Definition of material

The material is defined by command DEFI_MATERIAU as in the example below:

MATERBO=DEFI_MATERIAU (ELAS=_F (E=5.15000000E8,
NU=0.20,
RHO=2670.0,
ALPHA=0.,),
COMP_THM = “LIQU_AD_GAZ_VAPE”,
THM_LIQU=_F (RHO=1000.0,
UN_SUR_K=0.,
ALPHA=0.,
CP=0.0,
VISC=VISCOLIQ,
D_VISC_TEMP=DVISCOL,),
THM_GAZ=_F (MASS_MOL=0.01,
CP=0.0,
VISC=VISCOGAZ,
D_VISC_TEMP=ZERO,),
THM_VAPE_GAZ=_F (MASS_MOL=0.01,
CP=0.0,
VISC=VISCOGAZ,
D_VISC_TEMP=ZERO,),
THM_AIR_DISS=_F (
CP=0.0,
COEF_HENRY=HENRY
),
THM_INIT=_F (TEMP=300.0,
PRE1=0.0,
PRE2=1.E5,
PORO=1.,
PRES_VAPE=1000.0,
DEGR_SATU=0.4,),
THM_DIFFU=_F (R_GAZ=8.32,
RHO=2200.0,
CP=1000.0,
BIOT_COEF=1.0,
SATU_PRES=SATUBO,
D_SATU_PRES=DSATBO,
PESA_X=0.0,
PESA_Y=0.0,
PESA_Z=0.0,
PERM_IN=KINTBO,
PERM_LIQU=UNDEMI,
D_PERM_LIQU_SATU=ZERO,
PERM_GAZ=UNDEMI,
D_PERM_SATU_GAZ=ZERO,
D_PERM_PRES_GAZ=ZERO,
FICKV_T=ZERO,
FICKA_T=FICK,
LAMB_T=ZERO,
),);
Handbook of Utilization
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Code_Aster ®
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2.2.1 Key word factor ELAS

Definition of the constant linear elastic characteristics or functions of parameter “TEMP”.

E

Young modulus. It is checked that E 0.

NAKED

Poisson's ratio. One checks that - 1. naked 0.5.

ALPHA

Isotropic thermal dilation coefficient of the grains.

2.2.2 Single-ended spanner word COMP_THM

Allows to select as of the definition of material the mixing rate THM. The possible laws are

COMP_THM =/`LIQU_SATU `,

/`LIQU_GAZ `,

/`GAZ `,

/`LIQU_GAZ_ATM `,

/`LIQU_VAPE_GAZ `,

/`LIQU_AD_GAZ_VAPE `,


/`LIQU_VAPE `,
/“GAZ”

Law of reaction of a perfect gas i.e. checking the relation P/= RT/Mv where P is
pressure, density, Mv molar mass, R the constant of perfect gases and T
temperature (Cf. [R7.01.11] for more details). For an only saturated medium. Data
necessary of the field material are provided in operator DEFI_MATERIAU, under the word
key THM_GAZ.

/“LIQU_SATU”

Law of behavior for porous environments saturated by only one liquid (Cf. [R7.01.11] for more
details). The data necessary of the field material are provided in the operator
DEFI_MATERIAU, under key word THM_LIQ.

/“LIQU_GAZ_ATM”

Law of behavior for a porous environment unsaturated with a liquid and gas with pressure
atmospheric (Cf. [R7.01.11] for more details). Data necessary of the field material
are provided in operator DEFI_MATERIAU, under key words THM_LIQ and THM_GAZ.

/“LIQU_VAPE_GAZ”

Law of behavior for a porous environment unsaturated water/vapor/dry air with change with
phase (Cf. [R7.01.11] for more details). The data necessary of the field material are
provided in operator DEFI_MATERIAU, under key words THM_LIQ, THM_VAPE and THM_GAZ.

/“LIQU_AD_GAZ_VAPE”

Law of behavior for a porous environment unsaturated water/vapor/dry air/air dissolved with
phase shift (Cf. [R7.01.11] for more details). Data necessary of the field
material are provided in operator DEFI_MATERIAU, under key words THM_LIQ, THM_VAPE,
THM_GAZ and THM_AIR_DISS.
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/“LIQU_VAPE”

Law of behavior for porous environments saturated by a component present in liquid form
or vapor. with phase shift (Cf. [R7.01.11] for more details). Data
necessary of the field material are provided in operator DEFI_MATERIAU, under the words
keys THM_LIQ and THM_VAPE. This law is valid only for modelings of the type THVD.
/“LIQU_GAZ”

Law of behavior for a porous environment unsaturated liquid/gas without phase shift
(Cf [R7.01.11] for more details). The data necessary of the field material are provided
in operator DEFI_MATERIAU, under key words THM_LIQ and THM_GAZ.

The table below specifies the obligatory key words for under following commands in
function of the selected mixing rate.

Legends:
O: Key word Obligatoire

T: Obligatory key word in Thermique


: Key word Inutile for this type of mixing rate


LIQU_SATU
LIQU_GAZ
GAZ
LIQU_GAZ_AT
LIQU_VAPE_GAZ LIQU_AD_GAZ_VAPE LIQU_VAPE
M
THM_INIT
O
O
O
O
O
O
O
PRE1 O
O
O
O
O
O
O
PRE2

O


O
O

PORO O
O
O
O
O
O
O
TEMP T
O
O
T
O
O
O
PRES_VAPE




O
O
O
THM_DIFFU
O
O
O
O
O
O
O
R_GAZ

O
O

O
O
O
RHO O
O
O
O
O
O
O
BIOT_COEF O
O
O
O O
O O
PESA_X O
O
O
O
O O
O
PESA_Y O
O
O
O
O O
O
PESA_Z O
O
O
O
O O
O
SATU_PRES

O
I
O
O
O
O
D_SATU_PRES

O
I
O
O
O
O
PERM_LIQU
I
O
I
O
O
O
O
D_PERM_LIQU_SATU

O

O
O
O
O
PERM_GAZ

O


O
O
O
D_PERM_SATU_GAZ

O


O
O
O
D_PERM_PRES_GAZ

O


O
O
O
FICKV_T




O
O

FICKV_PV



FICKV_PG




FICKV_S





D_FV_T





D_FV_PG




FICKA_T



O

FICKA_PA



FICKA_PL



FICKA_S





D_FA_T





CP T
T
T
T
T
T
T
PERM_IN/PERM_END O
O O
O
O
O
O
LAMB_T T
T
T
T
T T
T
LAMB_S





LAMB_PHI




LAMB_CT




D_LB_T





D_LB_S





D_LB_PHI



THM_LIQU
O
O

O
O
O
O
RHO O
O

O
O
O
O
UN_SUR_K O
O

O O
O O
VISC O
O

O
O
O
O
D_VISC_TEMP O
O

O
O
O
O
ALPHA T
T

T
T
T
T
CP T
T

T
T
T
T
THM_GAZ

O
O
O
O
O
MASS_MOL
O
O
O O O
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VISC
O
O
O
O
O

D_VISC_TEMP
O
O
O O
O

CP
T
T
T
T
T

THM_VAPE_GAZ




O
O
O
MASS_MOL


O O O
CP



O
O
O
VISC



O
O
O
D_VISC_TEMP



O
O
O
THM_AIR_DISS





O

CP




O

COEF_HENRY




O


2.2.3 Key word factor THM_INIT

For all Hydro-Mécaniques the Thermo- behaviors, it makes it possible to describe a state of reference of
the structure (cf [R7.01.11] and [R7.01.14]). Its syntax is as follows:

THM_INIT = _F (



TEMP =
temp
,
[R]



PRE1

=
pre1
,
[R]



PRE2 =
pre2
,
[R]



PORO =
poro
,
[R]


PRES_VAPE =
pvap
, [R]




)

For including/understanding these data well, it is necessary to distinguish the unknown factors with the nodes, which we call
{}
U ddl and the values defined under key word THM_INIT which we call pref and T ref.

ux



uy

{U}
U
ddl

Z


=

ddl
PRE1

ddl
PRE 2
ddl
T




The significance of unknown factors PRE1 and PRE2 varies according to the models. By noting pw pressure
of water, pad pressure of dissolved air, plq pressure of liquid p = p + p, p, p pressure
lq
W
AD
have
vp
of vapor, p pressure of dry air and p = p + p total pressure of gas and p = p - p
have
G
have
vp
C
G
lq
capillary pressure (also called suction), one has the following significances of unknown factors PRE1 and
PRE2

Behavior LIQU_SATU LIQU_GAZ_ATM GAS LIQU_VAPE_GAZ
KIT

PRE1
p
- p
p
p = p - p
lq
lq
G
C
G
lq
PRE2


pg

Behavior LIQU_GAZ LIQU_VAPE
LIQU_AD_GAZ_VAPE
KIT
PRE1
p = p - p p
p = p - p
C
G
lq
lq
C
G
lq
PRE2
pg

pg
Table 2.2.3-1: contents of PRE1 and PRE2
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One will be able to refer to [§3.3.2.3] documentation of command STAT_NON_LINE
[U4.51.03].

One then defines the “total” pressures and the temperature by:

p
pddl
pref
;
T
Tddl Tref
=
+
=
+


All the values in input or output (boundary conditions or result of IMPR_RESU) are
nodal unknown factors ddl
ddl
p

and T
.

On the other hand in fact the pressures and the total air temperature are used in the laws of
p
R
D
dp
behavior
T
L
L
=
for perfect gases,
=
- 3 dT for the liquid and in
M


K
L
L
L
relation capillary saturation/pressure.

Let us note that the nodal values can be initialized by key word ETAT_INIT of the command
STAT_NON_LINE (cf 2.3).

The user must be very careful in the definition of the values of THM_INIT: indeed, the definition of
several materials with values different from the quantities defined under THM_INIT leads to
discontinuous values initial of the pressure and the temperature, which is not in fact not compatible
with the general processing which is made of these quantities. We thus advise with the user
following step:

· if there is initially a uniform field of pressure or temperature, it is informed
directly by key word THM_INIT,
· if there is a nonuniform field, one defines for example a reference by the key word
THM_INIT of command DEFI_MATERIAU, and the initial values compared to this
reference by key word ETAT_INIT of command STAT_NON_LINE (cf 2.3).

TEMP

Temperature of reference ref.
T
.
The value of the temperature of reference entered behind key word TEMP_REF of
order AFFE_MATERIAU is ignored.

PRE1

As seen in table 1:
For the behaviors: LIQU_SATU, and LIQU_VAPE pressure of liquid of reference.
For the behavior: GAZ pressure of standard gas.
For the behavior: LIQU_GAZ_ATM pressure of liquid of changed reference of sign.
For the behaviors: LIQU_VAPE_GAZ, LIQU_AD_GAZ_VAPE and LIQU_GAZ pressure
thin cable of reference.

PRE2

For the behaviors: LIQU_VAPE_GAZ, LIQU_AD_GAZ_VAPE and LIQU_GAZ and pressure of
standard gas.

Important remark:

One never should take a value of PRE2 equal to zero under penalty of problems
numerical.

PORO

Initial porosity.
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PRES_VAPE

Initial steam pressure for the behaviors: LIQU_VAPE_GAZ, LIQU_AD_GAZ_VAPE,
LIQU_VAPE and LIQU_GAZ.

Note:

The initial vapor pressure must be taken in coherence with the other data.
Very often, one leaves the knowledge of an initial state of hygroscopy. The degree
hygrometrical is the relationship between the steam pressure and the steam pressure
saturating at the temperature considered. One then uses the law of Kelvin which gives
pressure of the liquid according to the steam pressure, of the temperature and of
0
p
p
R
p

W -
saturating steam pressure:
W =
T ln
vp

ol
sat


. This relation is not
M
W
vp
p (T)
vp

valid that for isothermal evolutions. For evolutions with variation of
temperature, knowing a law giving the steam pressure saturating to

0
T -
5
.
273


2
+
7858
.
sat

31 559
.
+ 1354
.
(0T-
)
temperature T, for example:

p (T) 10
, and a degree
vp
0
=
5
.
273
0
from hygroscopy HR, one deduces from it the steam pressure thanks to p (T) = HR psat (T).
vp
0
vp
0
Moreover, one never should take a value of PRES_VAPE equalizes to zero.

2.2.4 Key word factor THM_LIQU

This key word relates to all behaviors THM utilizing a liquid (cf [R7.01.11]). Its
syntax is as follows:

THM_LIQU = _F (




RHO
=
rho
,
[R]




UN_SUR_K
=
usk
,
[R]




ALPHA
=
alp
,
[R]




CP
=
CP,
[R]




VISC =
VI,
[function
**]




D_VISC_TEMP =
dvi
, [function
**]




)

RHO

Density of the liquid for the pressure defined under key word PRE1 of the key word factor
THM_INIT.

UN_SUR_K

Opposite of the compressibility of the liquid: Kl.

ALPHA

Dilation coefficient of the liquid L
If pl indicates the pressure of the liquid, L its density and T the temperature, it
D
dp
behavior of the liquid is:
L
L
=
- 3 dT



K
L
L
L

CP

Specific heat with constant pressure of the liquid.
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VISC

[function **]

Viscosity of the liquid. Function of the temperature.

D_VISC_TEMP

[function **]

Derived from the viscosity of the liquid compared to the temperature. Function of the temperature.
The user must ensure coherence with the function associated with VISC.

2.2.5 Key word factor THM_GAZ

This key word factor relates to all behaviors THM utilizing a gas (cf [R7.01.11]).
For the behaviors utilizing at the same time a liquid and a gas, and when one takes into account
the evaporation of the liquid, the coefficients indicated here relate to dry gas. Properties of
vapor are indicated under key word THM_VAPE_GAZ. Its syntax is as follows:

THM_GAZ = _F (



MASS_MOL
=
Mgs
,
[R]


CP
=
CP,
[R]


VISC =
VI,
[function
**]



D_VISC_TEMP =
dvi
,
[function
**]





)

MASS_MOL

Mass molar dry gas. M gs
If pgs indicates the pressure of dry gas, gs its density, R the constant of gases
pgs
RT
perfect and T the temperature, the reaction of dry gas is: =
.
M
gs
gs

CP

Specific heat with constant pressure of dry gas.

VISC

[function **]

Viscosity of dry gas. Function of the temperature.

D_VISC_TEMP

[function **]

Derived compared to the temperature from viscosity from dry gas. Function of the temperature.
The user must ensure coherence with the function associated with VISC.

2.2.6 Key word factor THM_VAPE_GAZ

This key word factor relates to all behaviors THM utilizing at the same time a liquid and one
gas, and fascinating of account the evaporation of the liquid (cf [R7.01.11]). Coefficients indicated here
relate to the vapor. Syntax is as follows:

THM_VAPE_GAZ = _F
(



MASS_MOL =
m
,
[R]


CP
=
CP,
[R]


VISC =
VI,
[function
**]



D_VISC_TEMP =
dvi
, [function
**]







)
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MASS_MOL

Mass molar vapor. Mvp

CP


Specific heat with constant pressure of the vapor.

VISC

[function **]

Viscosity of the vapor. Function of the temperature.

D_VISC_TEMP

[function **]

Derived compared to the temperature from viscosity from the vapor. Function of the temperature.
The user must ensure coherence with the function associated with VISC.

2.2.7 Key word factor THM_AIR_DISS

This key word factor relates to fascinating behavior THM THM_AD_GAZ_VAPE of account
dissolution of the air in the liquid (cf [R7.01.11]). The coefficients indicated here relate to the air
dissolved. Syntax is as follows:

THM_AD_GAZ_VAPE = _F (




CP
=
CP,
[R]


COEF_HENRY
= KH
,
[function **]






)

CP

Specific heat with constant pressure of the dissolved air.

COEF_HENRY

Constant of Henry K, allowing to connect the molar concentration of dissolved air
H
ol
C (moles/m3) with the pressure of dry air:
AD
p
ol
have
C =

AD
K H

Note:

The constant of Henry that we use here expresses in Pa.m3.mol-1. In the literature it
exist various manners of writing the law of Henry. For example in the formulation of the book
loads of the platform Alliances [bib2]. The law of Henry is given
ol
P M
by A
have
have
=
with the concentration of air in water that have it can bring back to one
L
W
H M W
density such as A
=. H is a coefficient which is expressed out of Pa. It will be necessary in
L
AD
M
these cases to write equivalence
W
K = H

H
W

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2.2.8 Key word factor THM_DIFFU

Obligatory for all behaviors THM (cf [R7.01.11]). The user must ensure himself of
coherence of the functions and their derivative. Syntax is as follows:

THM_DIFFU = _F
(



R_GAZ
=
rgaz
,
[R]


RHO
=
rho
,
[R]


CP
=
CP,
[R]


BIOT_COEF
=
bio
,
[R]


SATU_PRES
=
sp,
[function]


D_SATU_PRES =
dsp
,
[function]


PESA_X
=
px,
[R]


PESA_Y
=
py,
[R]


PESA_Z
=
pz,
[R]


PERM_IN =
perm
,
[function]


PERM_LIQU
=
perml,
[function]


D_PERM_LIQU_SATU
=
dperm,
[function]


PERM_GAZ
=
permg,
[function]


D_PERM_SATU_GAZ
=
dpsg
,
[function]


D_PERM_PRES_GAZ
=
dppg
,
[function]


FICKV_T =
fvt
,
[function]


FICKV_PV =/
fvpv, [function]









/1
,
[DEFAUT]


FICKV_PG =/fvpg, [function]









/1
,
[DEFAUT]


FICKV_S =/fvs
,
[function]









/1
,
[DEFAUT]


D_FV_T
=
/
dfvt,
[function]









/0
,
[DEFAUT]


D_FV_PG =/dfvgp, [function]









/0
,
[DEFAUT]


FICKA_T =
conceited person
,
[function]


FICKA_PA =/fapv, [function]









/1
,
[DEFAUT]


FICKA_PL =/fapg, [function]









/1
,
[DEFAUT]


FICKA_S =/fas
,
[function]









/1
,
[DEFAUT]


D_FA_T
=
/
dfat,
[function]









/0
,
[DEFAUT]


LAMB_T
=
/
lambt
,
[function]









/0


[DEFAUT]


LAMB_S
=
/
lambs
,
[function]









/1
,
[DEFAUT]


LAMB_PHI =/lambp, [function]









/1
,
[DEFAUT]


LAMB_CT =/lambct
, [function]









/0
,
[DEFAUT]


D_LB_S
=
/
dlambs
,
[function]









/0
,
[DEFAUT]


D_LB_T
=
/
dlambt
,
[function]









/0
,
[DEFAUT]


D_LB_PHI =/dlambp
, [function]









/0
,
[DEFAUT]


SIGMA_T =
St,
[function]


D_SIGMA_T
=
dst
,
[function]
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PERM_G_INTR =
pgi
,
[function]




CHAL_VAPO
=
cv,
[function
**]


EMMAG
=
EM,
[R]



)

R_GAZ

Constant of perfect gases.

RHO

For the hydraulic behaviors initial homogenized density [R7.01.11].

CP

For the thermal behaviors, specific heat with constant constraint of the solid alone (of
grains).

Note:

Attention it acts here of the specific heat only and not of “C
”, as it is
p
fact for other thermal commands. The density of the grains is calculated in
the code starting from the homogenized density [R7.01.11].

BIOT_COEF

Coefficient of Biot.

SATU_PRES [function **]

For the unsaturated material behaviors (LIQU_VAPE_GAZ, LIQU_GAZ,
LIQU_GAZ_ATM), isotherm of saturation function of the capillary pressure.

Note:

For numerical reasons, it should be prevented that saturation reaches value 1. Also it is
very strongly recommended to multiply the capillary function (generally lain between 0
and 1) by 0,999.comme indicated on the command file given in example in appendix.

D_SATU_PRES

[function **]

For the unsaturated material behaviors (LIQU_VAPE_GAZ, LIQU_GAZ,
LIQU_GAZ_ATM), derived from saturation compared to the pressure.

PESA_X


Gravity according to X, used only if the modeling chosen in AFFE_MODELE includes 1 or 2
variables of pressure.

Note:

Gravity defined here is that used in the equation of Darcy only. When there is
mechanical calculations, gravity is also defined in AFFE_CHAR_MECA.Cette
notice applies of course for the three components of gravity.

PESA_Y

Gravity according to y, used only if the modeling chosen in AFFE_MODELE includes 1 or 2
variables of pressure.

PESA_Z

Gravity according to Z, used only if the modeling chosen in AFFE_MODELE includes 1 or 2
variables of pressure.
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PERM_IN

[function **]

Intrinsic permeability: function of porosity.
The permeability to the traditional direction K, whose dimension is that a speed is calculated
following way:
K K
K
rel
= int
G
L
µ
where Kint is the intrinsic permeability, Krel the relative permeability, µ
viscosity, L density of the liquid and G the acceleration of gravity.

PERM_LIQ

[function **]

Permeability relating to the liquid: function of saturation.

D_PERM_LIQ_SATU
[function **]

Derived from Perméabilité relating to the liquid compared to saturation: function of saturation.

PERM_GAZ

[function **]

Permeability relating to gas: function of the saturation and the gas pressure.

D_PERM_SATU_GAZ
[function **]

Derived from the permeability to gas compared to saturation: function of the saturation and of
gas pressure.

D_PERM_PRES_GAZ
[function **]

Derived from the permeability to gas compared to the gas pressure: function of the saturation and of
gas pressure.

FICKV_T

[function **]

For behaviors LIQU_VAPE_GAZ and LIQU_AD_GAZ_VAPE, multiplicative part of
coefficient of Fick function of the temperature for the diffusion of the vapor in the mixture
gas. The coefficient of Fick which can be a function of saturation, the temperature, pressure
gas and the steam pressure, one defines it as a product of 4 functions: FICKV_T,
FICKV_S, FICKV_PG, FICKV_VP. Seul FICKV_T is obligatory for the behaviors
LIQU_VAPE_GAZ and LIQU_AD_GAZ_VAPE.

FICKV_S

[function **]

For behaviors LIQU_VAPE_GAZ and LIQU_AD_GAZ_VAPE, multiplicative part of
coefficient of Fick function of saturation for the diffusion of the vapor in the gas mixture.
If this function is used, one recommends to take FICKV_S (1) = 0.

FICKV_PG

[function **]

For behaviors LIQU_VAPE_GAZ and LIQU_AD_GAZ_VAPE, multiplicative part of
coefficient of Fick function of the gas pressure for the diffusion of the vapor in the mixture
gas.

FICKV_PV

[function **]

For behaviors LIQU_VAPE_GAZ and LIQU_AD_GAZ_VAPE, multiplicative part of
coefficient of Fick function of the steam pressure for the diffusion of the vapor in
gas mixture.

D_FV_T
[function **]

For behaviors LIQU_VAPE_GAZ and LIQU_AD_GAZ_VAPE, derived from the coefficient
FICKV_T compared to the temperature.
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D_FV_PG

[function **]

For behaviors LIQU_VAPE_GAZ and LIQU_AD_GAZ_VAPE, derived from the coefficient
FICKV_PG compared to the gas pressure.

FICKA_T

[function **]

For the behavior LIQU_AD_GAZ_VAPE, multiplicative part of the coefficient of Fick function
temperature for the diffusion of the air dissolved in the liquid mixture. The coefficient of Fick
being able to be a function of saturation, the temperature, pressure of dissolved air and pressure of
liquid, one defines it as a product of 4 functions: FICKA_T, FICKA_S, FICKV_PA,
FICKV_PL. In the case of LIQU_AD_GAZ_VAPE, only FICKA_T are obligatory.

FICKA_S

[function **]

For the behavior LIQU_AD_GAZ_VAPE, multiplicative part of the coefficient of Fick function
saturation for the diffusion of the air dissolved in the liquid mixture.

FICKA_PA

[function **]

For the behavior LIQU_AD_GAZ_VAPE, multiplicative part of the coefficient of Fick function
pressure of air dissolved for the diffusion of the air dissolved in the liquid mixture.

FICKA_PL

[function **]

For the behavior LIQU_AD_GAZ_VAPE, multiplicative part of the coefficient of Fick function
pressure of liquid for the diffusion of the air dissolved in the liquid mixture.

D_FA_T
[function **]

For behavior LIQU_AD_GAZ_VAPE, derived from coefficient FICKA_T compared to
temperature.

LAMB_T
[function **]

Multiplicative part of the thermal conductivity of the mixture depend on the temperature
(cf [§2.2.9]). This operand is obligatory in the thermal case.

LAMB_S
[function **]

Multiplicative part (equalizes to 1 per defect) of the thermal conductivity of the mixture dependant on
saturation (cf [§2.2.9]).

LAMB_PHI

[function **]

Multiplicative part (equalizes to 1 per defect) of the thermal conductivity of the mixture dependant on
porosity (cf [§2.2.9]).

LAMB_CT

[function **]

Part of the thermal of the constant mixture and additive conductivity (cf [§2.2.9]). This constant
is equal to zero per defect.

D_LB_T
[function **]

Derived from the part of thermal conductivity of the mixture depend on the temperature by
report/ratio at the temperature.

D_LB_S
[function **]

Derived from the part of thermal conductivity of the mixture depend on saturation.

D_LB_PHI

[function **]

Derived from the part of thermal conductivity of the mixture depend on porosity.
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EMMAG

[function **]

Coefficient of storage. This coefficient is taken into account only in the cases of
modelings without mechanics.

2.2.9 Recapitulation of the functions of couplings and their dependence

The tables below points out the various functions and their possible dependences and
obligation.

Key word factor THM_LIQU


RHO
0
lq


1

UN_SUR_K

Klq

ALPHA
lq

CP
p
Clq

VISC
µ (T
lq
)


µ (T
lq
)

D_VISC_TEMP

T


Key word factor THM_GAZ


MASS_MOL
ol
M have

CP
p
Case

VISC
µ (T
have
)


µ (T
have
)

D_VISC_TEMP

T


Key word factor THM_VAPE_GAZ


MASS_MOL
ol
M
VP

CP
p
C
vp

VISC
µ (T
vp
)


µ (T
vp
)

D_VISC_TEMP

T


Key word factor THM_AIR_DISS


CP
p
C
AD

COEF_HENRY
K
H

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Key word factor THM_INIT


TEMP
initT

PRE1
init 1
P

PRE2
init 2
P

PORO
0


PRES_VAPE
0
pvp

2.2.9.1 Key word factor THM_DIFFU


R_GAZ
R

RHO
0
R

CP
S
C

BIOT_COEF
B

SATU_PRES
Slq (PC)


S
lq (PC)

D_SATU_PRES

p
C

PESA_X
m
Fx

PESA_Y
m
Fy

PESA_Z
m
Fz

PERM_IN
int
K
()

PERM_LIQU
rel
klq (Slq)


rel
K
lq (Slq)

D_PERM_LIQU_SATU

S
lq

PERM_GAZ
rel
kgz (Slq, pgz)


rel
K
gz (Slq, pgz)

D_PERM_SATU_GAZ

S
lq


rel
K
gz (Slq, pgz)

D_PERM_PRES_GAZ

p
gz

FICKV_T
F T (T)
vp

FICKV_S
F S (S)
vp

FICKV_PG
gz
F (P)
vp
G

FICKV_PV
vp
F (P)
vp
vp


F T

T
()

vp
D_FV_T

T

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gz
F
(P)

vp
gz
D_FV_PG

P
gz

FICKA_T
F T (T)
AD

FICKA_S
F S (S)
AD

FICKA_PA
AD
F (P)
AD
AD

FICKA_PL
lq
F (P)
AD
lq


F T

T
()

D_FA_T
AD

T


LAMB_T
T
(T)
T


T
T
()

D_LB_T
T

T


LAMB_PHI
T (
)



T
()

D_LB_PHI




LAMB_S
T
(S)
S


T
(S)

D_LB_S
S

S


LAMB_CT
T

CT

Note:

If there is thermics:
T
is a function of porosity, saturation and temperature and is given under
form product of three functions:
T
T
T
T
T
=
T


(

). (S

).
T
() + with
(T) (a.c. D
S
lq
T
cte
T
LAMB_T) obligatory and others
functions by defect taken equal to one, except T

.
cte = 0
For the coefficient of Fick of the gas mixture, in case LIQU_VAPE_GAZ and
vp
gz
T
S
LIQU_AD_GAZ_VAPE
F (P, P, T, S) = F (P). F (P). F (T). F (S) with
vp
vp
gz
vp
vp
vp
gz
vp
vp
F T (T) obligatory, other functions being taken by defect equal to one, and the derivative
vp
equal to zero. one will neglect the derivative compared to steam pressure and saturation.

In case LIQU_VAPE_GAZ_AD, the coefficient of Fick of the liquid mixture will be under
form: F (P, P, T, S) = F AD (P). F lq (P). F T (T). F S (S)
F T (T obligatory,
AD
AD
lq
AD
AD
AD
lq
AD
AD
, with
)
AD
other functions being taken by defect equal to one, and the derivative equalizes to zero. One
consider that the derivative compared to the temperature (the others are in any case taken
equal to zero).

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2.3
Initialization of calculation

To define an initial state, it is necessary to define a state of stresses (with the elements), unknown factors
nodal. and of the internal variables.

· In key word THM_INIT of DEFI_MATERIAU, one defines values of reference for
nodal unknown factors.
· By key word DEPL of the key word factor ETAT_INIT of command STAT_NON_LINE, one
affect the fields of initialization of the nodal unknown factors.
· By key word SIGM of the key word factor ETAT_INIT. command STAT_NON_LINE,
the fields of initialization of the constraints are affected.
· By key word VARI of the key word factor ETAT_INIT one affects (possibly) it
fields of initialization of the internal variables.

In order to specify the things, one recalls to which category of variables belong each
physical size (these physical sizes existing or not according to selected modeling):

Unknown factors
p, p, p, T, U, U, U
nodal
C
G
lq
X
y
Z
Constraints
,
at items xx
yy
zz
xy
xz
yz
p
of Gauss
m, M, MR. M, m, M
, M
M
, m, M
, M
M
,
W
W X
W y
W Z
vp
vp
vp
vp
have
have
X
y
Z
X
have y
have Z
m
m
m
m
m, M
, M
M
, H, H, H, H, Q, Q, Q, Q
AD
AD X
AD y
AD Z
W
vp
have
AD
X
y
Z
Variables
, p, S
interns
lq
vp
lq

The correspondence between name of Aster component and physical size is clarified in
[§Annexe 1].
The initialization of the nodal unknown factors as well as the difference between initial state and state of reference have
summer described and detailed in [§2.2.3]. It is pointed out nevertheless that
ddl
ref.
p = p
+ p for the pressures
ddl
PRE1 and PRE2 and
ref.
T = T
+ T for the temperatures, where ref.
p and ref.
T
are defined under the key word
THM_INIT of command DEFI_MATERIAU.

Key word DEPL of the key word factor ETAT_INIT of command STAT_NON_LINE defines the values
initial of {} ddl
U
. The initial values of the densities of the vapor and the dry air are
defined starting from the initial values of the vapor and gas pressures (values read under the key word
THM_INIT of command DEFI_MATERIAU). It is noticed that, for displacements,
decomposition
ddl
ref.
U = U
+ U is not made: key word THM_INIT of command DEFI_MATERIAU
thus does not allow to define initial displacements. The only way of initializing displacements
is thus to give them an initial value by the key word factor ETAT_INIT of the command
STAT_NON_LINE.
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Concerning the constraints, the fields to be informed are the constraints indicated in appendix I
according to selected modeling.
Initial values of the enthali, which belong to the generalized constraints are defined in
to leave key word SIGM of the key word factor ETAT_INIT of command STAT_NON_LINE. The introduction
initial conditions is very important, for the enthali. In practice, one can reason in
considering that one has three states for the fluids:

· the state running,
· the state of reference: it is that of the fluids in a free state. In this state of reference, one can
to consider that the enthali are null,
· the initial state: it must be in thermodynamic balance. For the enthali of water and
vapor one will have to take:

init
init m
pw - ref.
init
pl
pw - p
hw =
=
atm
W
W
init m
vp
H = L (init
T
) = heat
vaporisati

of

latent

one
init m
have
H = 0
init m
AD
H
= 0

and with L (T) = 2500800 -
(
2443 T - 273.15) J/kg

Note:

The initial vapor pressure will have to be taken in coherence with these choices (cf [§2.2.3]).

Concerning the mechanical constraints, the partition of the constraints in constraints total and effective
is written:

= '
+ 1
p

where is the total constraint, a.c. D that which checks:
(
Div) + m
RF = 0
is the effective constraint. For the laws of effective constraints, it checks:
1
D = F (
D -
= +T
0dT,), where
(U U) and represents the internal variables.
2
is calculated according to the water pressures. The adopted writing is incremental and, if one
p
wants that the value of is coherent with value ref.
p (
p
PRE1) definite under the key word
THM_INIT, it is necessary to initialize by the key word
p
SIGM of the key word factor ETAT_INIT of the command
STAT_NON_LINE.
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Warning:

In the case of fields of pressures or temperatures heterogeneous, it is necessary to ensure “manually
continuity “enters the fields. That Ci is not ­ for the moment ­ not taken into account automatically.
In the current state, the degrees of freedom (ddl) to the nodes located at the interface between two meshs
take the value of the ddl material initialized in the last as on the figure. Consequently it
materials affected in first is found with heterogeneous values of displacements. To ensure
continuity, it is necessary to impose on the nodes medium (in grayed on [Figure 2.3-a]) an average value enters
two materials. This processing necessary in is seen of a correct postprocessing but does not have
of impact on calculation in him even.

Value with the node of the ddl re-entered for the mesh

M1 (affected in first)

M2
M1

Value with the node of the ddl re-entered for the mesh

M2 (affected as a second)

Value to be modified (average between M1 etM2)

Appear 2.3-a: Gestion of discontinuities between two meshs

If one refers to the example presented in [§Annexe 3], the fields of displacements initialized in
ETAT_INIT are then defined for example in the following way:

CHAMNO=CREA_CHAMP (MAILLAGE=MAIL,
OPERATION=' AFFE',
TYPE_CHAM=' NOEU_DEPL_R',
AFFE= (_F (TOUT=' OUI',
NOM_CMP=' TEMP',
VALE=0.0,),
_F (GROUP_NO=' SURFBO',
NOM_CMP=' PRE1',
VALE=7.E7,),
_F (GROUP_NO=' SURFBG',
NOM_CMP=' PRE1',
VALE=3.E7,),
_F (NOEUD= (“NO300”, “NO296”),
NOM_CMP=' PRE1',
VALE=5.E7,),
_F (GROUP_NO=' SURFBO',
NOM_CMP=' PRE2',
VALE=0.0,),
_F (GROUP_NO=' SURFBG',
NOM_CMP=' PRE2',
VALE=0.0,),),);

And stress fields in the following way:

SIGINIT=CREA_CHAMP (MAILLAGE=MAIL,
OPERATION=' AFFE',
TYPE_CHAM=' CART_SIEF_R',
AFFE= (_F (GROUP_MA=' BO',
NOM_CMP=
(“SIXX”, “SIYY”, “SIZZ”, “SIXY”, “SIXZ”,
“SIYZ”, “SIP”, “M11”, “FH11X”, “FH11Y”, “ENT11”,
“M12”, “FH12X”, “FH12Y”, “ENT12”,
“QPRIM”, “FHTX”, “FHTY”, “M21”,
“FH21X”, “FH21Y”, “ENT21”,
“M22”, “FH22X”, “FH22Y”, “ENT22”,),
VALE=
(0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 2500000.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0., 0., 0., 0.),),),);
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2.4
Loadings and boundary conditions

All the boundary conditions or loading are affected via command AFFE_CHAR_MECA
[U4.44.01]. The loadings are then activated by the key word factor EXCIT of the command
STAT_NON_LINE.

In a traditional way, two types of boundary conditions are possible:

· Conditions of the Dirichlet type which consist in imposing on part of border of
values fixed for principal unknown factors belonging to {} ddl
U
(and not
ddl
init
U = U + U)
for that one uses key word factor DDL_IMPO of AFFE_CHAR_MECA.
· Conditions of the Neuman type which consist in imposing values on the “quantities
dual “, either by not saying anything (null flows), or in their giving a value via the key words
FLUN, FLUN_HYDR1 and FLUN_HYDR2 of the key word factor FLUX_THM_REP of the command
AFFE_CHAR_MECA. This flow is then multiplied by a function of time (by defect equalizes with
1) in under the word key one EXCIT of command STAT_NON_LINE. Mechanical conditions
in total constraints .n is they given via PRES_REP of the command
AFFE_CHAR_MECA. One will refer to the documentation of this command to know some
possibilities.

From a syntactic point of view the conditions of Dirichlet thus apply as to the example
according to

DIRI=AFFE_CHAR_MECA (MODELE=MODELE,
DDL_IMPO= (_F (GROUP_NO=' GAUCHE',
TEMP=0.0,),
_F (TOUT=' OUI',
PRE2=0.0,),
_F (GROUP_NO=' GAUCHE',
PRE1=0.0,),
_F (TOUT=' OUI',
DX=0.0,),
_F (TOUT=' OUI',
DY=0.0,),
_F (TOUT=' OUI',
DZ=0.0,),
),)

For the conditions of Neuman, syntax will be then as on the following example:

NEU1=AFFE_CHAR_MECA (MODELE=MODELE,
FLUX_THM_REP=_F (GROUP_MA=' DROIT',
FLUN=200.,
FLUN_HYDR1=0.0,
FLUN_HYDR2=0.0),);
NEU2=AFFE_CHAR_MECA (MODELE=MODELE,
PRES_REP=_F (GROUP_MA=' DROIT',
PRES=2.,),);

One defines then the multiplicative function which one wants to apply, for example with NEU1:

FLUX=DEFI_FONCTION (NOM_PARA=' INST',
VALE=
(0.0, 386.0,
315360000.0, 312.0,
9460800000.0, 12.6),);
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The loadings are then activated in STAT_NON_LINE via key word EXCIT in the manner
following:
EXCIT= (
_F (CHARGE=DIRI,),
_F (CHARGE=NEU2,),
_F (CHARGE=NEU1,
FONC_MULT=FLUX,),
),

FLUN corresponds to the value of the heat flow. FLUN_HYDR1 and FLUN_HYDR2 correspond to
values of the hydraulic flows associated pressures PRE1 and PRE2. If there is no ambiguity for
thermics or mechanics, on the other hand unknown factors principal hydraulic PRE1 and PRE2
change according to the selected coupling. As it below is pointed out

Behavior
LIQU_SATU
LIQU_VAPE LIQU_GAZ_ATM
GAZ
LIQU_VAPE_GAZ


LIQU_GAZ
LIQU_AD_GAZ_VA
EP
PRE1
p
p
- p
p
p = p - p
lq
lq
lq
G
C
G
lq
PRE2



pg

Associated flows are:

For
ext.
PRE1, FLUN_HYDR1: (M + M
N
. = M
+ M
W
vp)
ext.
W
vp
For
ext.
PRE2, FLUN_HYDR2: (M
+ M N
. = M
+ M
AD
have)
ext.
AD
have

We thus will summarize the various possibilities by distinguishing the case where one imposes values on
PRE1 and/or PRE2 and that where one works on combinations of the 2. It is announced that one can of course
to have various types of boundary conditions according to the pieces of border (groups of nodes
or of meshs) which one treats. For a more complete and more detailed outline in the way in which are
treated the boundary conditions in the case unsaturated, one will refer to the note reproduced in
appendix 2.

· Case of the boundary conditions utilizing unknown factors principal PRE1 and
PRE2

One summarizes here the usual case where one imposes value on PRE1 and/or PRE2.

- Dirichlet on PRE1 and Dirichlet on PRE2
The user imposes a value on PRE1 and PRE2; flows are results of
calculation.
- Dirichlet on PRE1 and Neuman on PRE2
The user imposes a value on PRE1 and a value with flow associated with PRE2 in
saying anything on PRE2 or by giving a value to FLUN_HYDR2.
- Dirichlet on PRE2 and Neuman on PRE1
The user imposes a value on PRE2 and a value with flow associated with PRE1 in
saying anything on PRE1 or by giving a value to FLUN_HYDR1.
- Neuman on PRE2 and Neuman on PRE1
Two flows are imposed either by not saying anything on PRE1 and/or PRE2 (null flows)
maybe by giving a value to FLUN_HYDR1.et/ou FLUN_HYDR2
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· Case of the boundary conditions utilizing a linear relation between
unknown factors principal PRE1 and PRE2

It is also possible to handle linear combinations of PRE1 and PRE2. It is necessary
however to handle that with precaution so as to start from a correctly posed problem.
The syntax of this operator is detailed in the documentation of AFFE_CHAR_MECA,
the example below into famous this type of condition:

P_DDL=AFFE_CHAR_MECA (MODELE=MODELE,
LIAISON_GROUP= (_F (
GROUP_NO_1= “BORDS”,
GROUP_NO_2= “BORDS”,
DDL_1=' PRE1',
DDL_2=' PRE2',
COEF_MULT_1 = X,
COEF_MULT_2 = Y.,
COEF_IMPO =z,),),
);

This command means that on the border defined by the group of nodes “BORDS”, them
pressures PRE1 and PRE2 are connected by the linear relation
X PRE1 + y PRE2 = Z

Note:

Flows imposed are scalar quantities which can apply to a line
or a surface interns with the modelled solid. In this case, these boundary conditions
correspond to a source.

2.5
Nonlinear calculation

Calculation is carried out by command STAT_NON_LINE as in the example below:

U0=STAT_NON_LINE (MODELE=MODELE,
CHAM_MATER=CHMAT0,
EXCIT= (
_F (CHARGE=T_IMP,),
_F (CHARGE=CALINT,
FONC_MULT=FLUX,),),
COMP_INCR=_F (RELATION=' KIT_THHM',
RELATION_KIT= (“ELAS”, “LIQU_GAZ”
, “HYDR_UTIL”),),
RECH_LINEAIRE =_F (RESI_LINE_RELA = 1.E-3,
RHO_MIN = 0.1,
RHO_MAX = 0.2,
ITER_LINE_MAXI = 3,),
ETAT_INIT=_F (DEPL=CHAMNO,
SIGM=SIGINIT),
INCREMENT=_F (LIST_INST=INST1,),
NEWTON=_F (MATRICE=' TANGENTE', REAC_ITER=10,),
CONVERGENCE=_F (RESI_GLOB_MAXI=1.0000000000000001E-05,
ITER_GLOB_MAXI=150,
ARRET=' NON',
ITER_INTE_MAXI=5,),
ARCHIVAGE=_F (PAS_ARCH=1,),);

To this command one assigns the model (key word MODELE), it/the materials (key word CHAM_MATER),
/the loadings (key word EXCIT) and the initial state (key word ETAT_INIT) which one defined by all
commands described previously.
For general information concerning this command and his syntax, one will refer to its
documentation. It is specified just that the method of calculation is a method of Newton.
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Caution:

Under the key word factor NEWTON, one must put a matrix of the type “TANGENTE” and not
“ELASTIQUE”.

One speaks here only about what is specific to calculations THM with knowing the key words factors RELATION
and RELATION_KIT of the key word COMP_INCR which are closely dependant.

RELATION is indicated by relations of the types which make it possible to solve
at the same time from two to four equilibrium equations. The equations considered depend on
suffix with the following rule:

M indicates the mechanical equilibrium equation,
T indicates the thermal equilibrium equation,
H indicates a hydraulic equilibrium equation.
V indicates the presence of a phase in form vapor (in addition to the liquid)

Only one letter H means that the porous environment is saturated (only one variable of pressure p), by
example either of gas, or of liquid, or of a liquid mixture/gas (of which the pressure of gas is
constant).
Two letters H mean that the porous environment is not saturated (two variables of pressure p), by
example a liquid mixture/vapor/gas.
The presence of two letters HV means that the porous environment is saturated by a component (with
practical of water), but that this component can be in liquid form or vapor. There is not whereas one
conservation equation of this component, therefore only one degree of freedom pressure, but there is a flow
liquid and a flow vapor. The possible relations are then the following ones:

/“KIT_HM”
/“KIT_THM”
/“KIT_HHM”
/“KIT_THH”
/“KIT_THV”
/“KIT_THHM”

The table below summarizes to which kit each modeling corresponds:

KIT_HM
D_PLAN_HM, D_PLAN_HMD, AXIS_HM, AXIS_HMD, 3D_HM, 3D_HMD
KIT_THM
D_PLAN_THM, D_PLAN_THMD, AXIS_THM, AXIS_THMD, 3D_THM, 3D_THMD
KIT_HHM
D_PLAN_HHM, D_PLAN_HHMD, AXIS_HHM, AXIS_HHMD, 3D_HHM, 3D_HHMD,
D_PLAN_HH2MD, AXIS_HH2MD, 3d_HH2MD
KIT_THH
D_PLAN_THH, D_PLAN_THHD, AXIS_THH, AXIS_THHD, 3D_THH, 3D_THHD,
D_PLAN_THH 2D, AXIS_THH 2D, 3D_THH 2D
KIT_THV
D_PLAN_THVD, AXIS_THVD, 3D_THVD
KIT_THHM
D_PLAN_THHM, D_PLAN_THHMD, AXIS_THHM, AXIS_THHMD, 3D_THHM,
3d_THHMD, D_PLAN_THH2MD, AXIS_THH2MD, 3d_THH2MD

For each modelled phenomenon (thermal and/or mechanical and/or hydraulic), one must specify
in RELATION_KIT:

· The mechanical model of behavior of the skeleton if there is mechanical modeling (M),

/“ELAS”
/“CJS”
/“LAIGLE”
/“ELAS_THM”
/“CAM_CLAY”
/“DRUCKER_PRAGER”
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· The behavior of the liquids/gas, (the same one as that indicated in COMP_THM under
DEFI_MATERIAU, cf [§2.2.2])

/“LIQU_SATU”
/“LIQU_GAZ”
/“GAZ”
/“LIQU_GAZ_ATM”
/“LIQU_VAPE_GAZ”
/“LIQU_AD_GAZ_VAPE”
/“LIQU_VAPE”

· Moreover in all the cases, one must imperatively inform: HYDR_UTIL under
RELATION_KIT (this key word makes it possible to inform the curve of saturation and its derivative in
function of the capillary pressure as well as the relative permeability and its derivative according to
saturation).

If one mentions the example above, one deals with in a coupled way a hydro-mechanical thermo problem
for a porous environment unsaturated with LIQU_GAZ like behavior with the liquid, and a law
rubber band like mechanical behavior.

Caution:

According to chosen, all the behaviors are not licit (for example if one
chosen porous environments unsaturated, one cannot affect a behavior of the gas type
perfect). all the possible combinations are summarized below

For relation KIT_HM:

(“ELAS” “GAS”
“HYDR_UTIL”)
(“CJS”
“GAZ”
“HYDR_UTIL”)
(“LAIGLE”
“GAZ”
“HYDR_UTIL”)
(“CAM_CLAY” “GAS”
“HYDR_UTIL”)
(“ELAS” “LIQU_SATU” “HYDR_UTIL”)
(“CJS”
“LIQU_SATU” “HYDR_UTIL”)
(“LAIGLE”
“LIQU_SATU” “HYDR_UTIL”)

(“CAM_CLAY” “LIQU_SATU” “HYDR_UTIL”)
(“ELAS” “LIQU_GAZ_ATM” “HYDR_UTIL”)
(“CJS”
“LIQU_GAZ_ATM” “HYDR_UTIL”)
(“LAIGLE”
“LIQU_GAZ_ATM” “HYDR_UTIL”)
(“CAM_CLAY” “LIQU_GAZ_ATM” “HYDR_UTIL”)

For relation KIT_THM:

(“ELAS” “GAS”



“HYDR_UTIL”)
(“CJS”



“GAZ”



“HYDR_UTIL”)
(“LAIGLE”

“GAZ”


“HYDR_UTIL”)
(“CAM_CLAY”

“GAZ”


“HYDR_UTIL”)
(“ELAS”

“LIQU_SATU”

“HYDR_UTIL”)
(“CJS”


“LIQU_SATU”

“HYDR_UTIL”)
(“LAIGLE”

“LIQU_SATU”

“HYDR_UTIL”)
(“CAM_CLAY”

“LIQU_SATU”

“HYDR_UTIL”)
(“ELAS” “LIQU_GAZ_ATM” “HYDR_UTIL”)
(“CJS”



“LIQU_GAZ_ATM” “HYDR_UTIL”)
(“LAIGLE”

“LIQU_GAZ_ATM”

“HYDR_UTIL”)
(“CAM_CLAY”

“LIQU_GAZ_ATM”

“HYDR_UTIL”)
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For relation KIT_HHM:

(“ELAS” “LIQU_GAZ”



“HYDR_UTIL”)
(“CJS”
“LIQU_GAZ”



“HYDR_UTIL”)
(“LAIGLE”
“LIQU_GAZ”



“HYDR_UTIL”)
(“CAM_CLAY” “LIQU_GAZ”



“HYDR_UTIL”)
(“ELAS” “LIQU_VAPE_GAZ”



“HYDR_UTIL”)
(“CJS”
“LIQU_VAPE_GAZ”



“HYDR_UTIL”)
(“LAIGLE”
“LIQU_VAPE_GAZ”



“HYDR_UTIL”)
(“CAM_CLAY” “LIQU_VAPE_GAZ”



“HYDR_UTIL”)
(“ELAS” “LIQU_AD_GAZ_VAPE”

“HYDR_UTIL”)
(“CJS”
“LIQU_AD_GAZ_VAPE”
“HYDR_UTIL”)
(“LAIGLE”
“LIQU_AD_GAZ_VAPE”
“HYDR_UTIL”)
(“CAM_CLAY” “LIQU_AD_GAZ_VAPE”
“HYDR_UTIL”)

For relation KIT_THH:

(“LIQU_GAZ” “HYDR_UTIL”)
(“LIQU_VAPE_GAZ”
“HYDR_UTIL”)
(“LIQU_AD_GAZ_VAPE” “HYDR_UTIL”)

For relation KIT_THV:

(“LIQU_VAPE”
“HYDR_UTIL”)

For relation KIT_THHM:

(“ELAS” “LIQU_GAZ”
“HYDR_UTIL”)
(“CJS”



“LIQU_GAZ”
“HYDR_UTIL”)
(“LAIGLE”



“LIQU_GAZ”
“HYDR_UTIL”)
(“CAM_CLAY”


“LIQU_GAZ” “HYDR_UTIL”)
(“ELAS” “LIQU_VAPE_GAZ”
“HYDR_UTIL”)
(“CJS”




“LIQU_VAPE_GAZ” “HYDR_UTIL”)
(“LAIGLE”


“LIQU_VAPE_GAZ”

“HYDR_UTIL”)
(“CAM_CLAY”


“LIQU_VAPE_GAZ” “HYDR_UTIL”)
(“ELAS” “LIQU_AD_GAZ_VAPE”
“HYDR_UTIL”)
(“CJS”




“LIQU_AD_GAZ_VAPE” “HYDR_UTIL”)
(“LAIGLE”


“LIQU_AD_GAZ_VAPE” “HYDR_UTIL”)
(“CAM_CLAY”


“LIQU_AD_GAZ_VAPE” “HYDR_UTIL”)

Note:

In the event of problem of convergence it can be very useful to activate linear search
as indicated in the example given at the head of this section. Linear search
do not improve however systematically convergence, it is thus to handle with
precaution.

2.6
postprocessing

The post processing data in THM does not vary a post usual Aster processing. One recalls
just that for any impression of the values which are not the nodal unknown factors, it is necessary
to calculate these values by the command CALC_ELEM whose one gives an example hereafter.

For the constraints:

U0=CALC_ELEM (reuse =U0,
MODELE=MODELE,
CHAM_MATER=CHMAT0,
TOUT_ORDRE=' OUI',
OPTION= (“SIEF_ELNO_ELGA”),
RESULTAT=U0,);
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For the internal variables:

U0=CALC_ELEM (reuse =U0,
MODELE=MODELE,
CHAM_MATER=CHMAT0,
TOUT_ORDRE=' OUI',
OPTION= (“VARI_ELNO_ELGA”),
RESULTAT=U0,);

It should however be recalled that all the values of displacements at outputs correspond to ddl
U
and
not
ddl
ref.
U = U
+ U.

It is also important to know the name of the constraints and the numbers of the internal variables.
All that is consigned in appendix I.
Thus the following example makes it possible to print the liquid water mass on the group of nodes HAUT to all
moments.

TAB1=POST_RELEVE_T (ACTION=_F (INTITULE=' CONT',
GROUP_NO= (“HIGH”),
RESULTAT=U0,
NOM_CHAM=' SIEF_ELNO_ELGA',
TOUT_ORDRE=' OUI',
NOM_CMP= (“M11”),
OPERATION=' EXTRACTION',),);

IMPR_TABLE (TABLE=TAB1,
FICHIER=' RESULTAT',
FORMAT=' AGRAF',
PAGINATION=' INST',
NOM_PARA= (“INST”, “COOR_X”, “M11”),);

The following example makes it possible to print the values of porosity to node 1 and the first moment.

TAB2=POST_RELEVE_T (ACTION=_F (INTITULE=' DEPL',
NOEUD=' NO1',
RESULTAT=U0,
NOM_CHAM=' VARI_ELNO_ELGA',
NUME_ORDRE=1,
NOM_CMP= (“V2”),
OPERATION=' EXTRACTION',),);
IMPR_TABLE (TABLE=TAB2,
FICHIER=' RESULTAT',
FORMAT=' AGRAF',
PAGINATION=' INST',
NOM_PARA= (“INST”, “COOR_X”, “V2”),);

Concerning the layout of isovaleurs IDEAS as GIBI are the two tools used.

2.6.1 Isovaleurs with Gibi

A file .cast readable by commands GIBI east creates via command IMPR_RESU as on
the example below:

IMPR_RESU (RESU=_F (FORMAT=' CASTEM',
RESULTAT=U0,
MAILLAGE=MAIL,
NUME_ORDRE=1,),),


The file obtained is then read by a file of processing. An example of files gibi of processing
data is in [§Annexe 4].
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2.6.2 Isovaleurs with IDEAS

A file .unv readable by IDEAS is created via command IMPR_RESU with format IDEAS as on
the example below:

IMPR_RESU (RESU=_F (FORMAT=' IDEAS',
RESULTAT=U0,
MAILLAGE=MAIL,
NUME_ORDRE=1,),),


3 Bibliography

[1]
Catsius Clay project. Calculation and testing off behavior off unsaturated clay have barrier in
radioactive waste repositories.
[2]
Card-index of model of thermal reference ­ Couplage hydraulic ANDRA-CNT ACSS 02-006

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Internal appendix 1 Contraintes generalized and variables

Constraints:

Number
Name of Aster component
Contents Modelings
1
SIXX

So mechanical (..M…)
xx
2
SIYY

So mechanical (..M…)
yy
3
SIZZ

So mechanical (..M…)
zz
4
SIXY

So mechanical (..M…)
xy
5
SIXZ

So mechanical (..M…)
xz
6
SIYZ

So mechanical (..M…)
yz
7
SIP

So mechanical (..M…)
p
8
M11
m
In all the cases
W
9
FH11X
M
In all the cases
W X
10
FH11Y
M

In all the cases
W y
11
FH11Z
M
In all the cases
W Z
12
ENT11
m
H
In all the cases
W
13
M12
m
If 2 unknown pressures (..HH…)
vp
14
FH12X
M

If 2 unknown pressures (..HH…)
vp X
15
FH12Y
M

If 2 unknown pressures (..HH…)
vp

y
16
FH12Z
M

If 2 unknown pressures (..HH…)
vp Z
17
ENT12
m
H
If 2 unknown pressures (..HH…)
vp
18
M21
m
If 2 unknown pressures (..HH…)
have
19
FH21X
M

If 2 unknown pressures (..HH…)
have X
20
FH21Y
M

If 2 unknown pressures (..HH…)
have y
21
FH21Z
M

If 2 unknown pressures (..HH…)
have Z
22
ENT21
m
H
If 2 unknown pressures (..HH…)
have
18
M22
m
If modeling of the dissolved air (… HH2…)
AD
19
FH22X
M

If modeling of the dissolved air (… HH2…)
AD X
20
FH22Y
M

If modeling of the dissolved air (… HH2…)
AD y
21
FH22Z
M

If modeling of the dissolved air (… HH2…)
AD Z
22
ENT22
m
H
If modeling of the dissolved air (… HH2…)
AD
23
QPRIM
Q'
So thermal

24
FHTX
Q
So thermal
X
25
FHTY
Q
So thermal
y
26
FHTZ
Q
So thermal
Z
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In the case without mechanics, the variables internal:

Number
Name component Aster
Contents
1 V1
0
-
lq
lq
2 V2
0
-
3 V3
0
p - p
vp
vp
4 V4
S
lq

In the case with mechanics the first numbers will be those corresponding to mechanics (V1 in
elastic case, V1 and following for plastic models). The number of the variables intern above will have
then to be incremented of as much.

Appendix 2 Exemple I of command file

# EXAMPLE OF CALCULATION AXIS_THH2MD

DEBUT ();
PRE_GIBI ();
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# # # # # # # # # # # # # # # # # # # # # # # # # # # #



INST1=DEFI_LIST_REEL (DEBUT=0.0,
INTERVALLE= (
_F (JUSQU_A=500000000., NOMBRE=50,),
_F (JUSQU_A=2000000000., NOMBRE=20,),
),);

MAIL=LIRE_MAILLAGE ();

MAIL=DEFI_GROUP (reuse =MAIL,
MAILLAGE=MAIL,
CREA_GROUP_NO= (_F (GROUP_MA=' BAS',),
_F (GROUP_MA=' HAUT',),
_F (GROUP_MA=' GAUCHE',),
_F (GROUP_MA=' DROIT',),
_F (GROUP_MA=' BO',),
),);

MODELE=AFFE_MODELE (MAILLAGE=MAIL,
AFFE=_F (TOUT=' OUI',
PHENOMENE=' MECANIQUE',
MODELISATION=' AXIS_THH2MD',),);
#
#

UN=DEFI_CONSTANTE (VALE=1.0,);
UNDEMI=DEFI_CONSTANTE (VALE=0.5,);

ZERO=DEFI_CONSTANTE (VALE=0.0,);

VISCOLIQ=DEFI_CONSTANTE (VALE=1.E-3,);

VISCOGAZ=DEFI_CONSTANTE (VALE=1.E-03,);

DVISCOL=DEFI_CONSTANTE (VALE=0.0,);

DVISCOG=DEFI_CONSTANTE (VALE=0.0,);

LI2=DEFI_LIST_REEL (DEBUT=-1.E9,
INTERVALLE= (
_F (JUSQU_A=1.E9,
NOMBRE=500,),),);

LI1=DEFI_LIST_REEL (DEBUT=0.10000000000000001,
INTERVALLE=_F (JUSQU_A=0.98999999999999999,
PAS=1.E-2,),);

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# LIMITATION OF SATURATION MAX (<1)
# CONSTBO = DEFI_CONSTANTE (VALE: 0.99);
#


SLO = FORMULA (REAL = ''' (REAL:PCAP) =
0.4 ''');

SATUBO=CALC_FONC_INTERP (FONCTION=SLO,
LIST_PARA=LI2,
NOM_PARA=' PCAP',
PROL_GAUCHE=' LINEAIRE',
PROL_DROITE=' LINEAIRE',
INFO=2,);

DSATBO=DEFI_CONSTANTE (VALE=0.,);
#

#
# COEF. FICK
#

FICK=DEFI_CONSTANTE (VALE=3.E-10,);

KINTBO=DEFI_CONSTANTE (VALE=9.9999999999999995E-19,);
HENRY=DEFI_CONSTANTE (VALE=50000.,);

MATERBO=DEFI_MATERIAU (ELAS=_F (E=5.15000000E8,
NU=0.20000000000000001,
RHO=2670.0,
ALPHA=0.,),
COMP_THM = “LIQU_AD_GAZ_VAPE”,
THM_LIQU=_F (RHO=1000.0,
UN_SUR_K=0.,
ALPHA=0.,
CP=0.0,
VISC=VISCOLIQ,
D_VISC_TEMP=DVISCOL,),
THM_GAZ=_F (MASS_MOL=0.01,
CP=0.0,
VISC=VISCOGAZ,
D_VISC_TEMP=ZERO,),
THM_VAPE_GAZ=_F (MASS_MOL=0.01,
CP=0.0,
VISC=VISCOGAZ,
D_VISC_TEMP=ZERO,),
THM_AIR_DISS=_F (
CP=0.0,
COEF_HENRY=HENRY
),
THM_INIT=_F (TEMP=300.0,
PRE1=0.0,
PRE2=1.E5,
PORO=1.,
PRES_VAPE=1000.0,
DEGR_SATU=0.4,),
THM_DIFFU=_F (R_GAZ=8.32,
RHO=2200.0,
CP=1000.0,
BIOT_COEF=1.0,
SATU_PRES=SATUBO,
D_SATU_PRES=DSATBO,
PESA_X=0.0,
PESA_Y=0.0,
PESA_Z=0.0,
PERM_IN=KINTBO,
PERM_LIQU=UNDEMI,
D_PERM_LIQU_SATU=ZERO,
PERM_GAZ=UNDEMI,
D_PERM_SATU_GAZ=ZERO,
D_PERM_PRES_GAZ=ZERO,
FICKV_T=ZERO,
FICKA_T=FICK,
LAMB_T=ZERO,
),);

CHMAT0=AFFE_MATERIAU (MAILLAGE=MAIL,
AFFE= (_F (GROUP_MA=' BO',
MATER=MATERBO,),
),);

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CHAMNO=CREA_CHAMP (MAILLAGE=MAIL,
OPERATION=' AFFE',
TYPE_CHAM=' NOEU_DEPL_R',
AFFE= (_F (TOUT=' OUI',
NOM_CMP=' TEMP',
VALE=0.0,),
_F (TOUT=' OUI',
NOM_CMP=' PRE2',
VALE=1000.0,),
_F (TOUT=' OUI',
NOM_CMP=' PRE1',
VALE=1.E6,),
),);

TIMP=AFFE_CHAR_MECA (MODELE=MODELE,
DDL_IMPO= (_F (TOUT=' OUI',
TEMP=0.0,),
_F (GROUP_NO= (“HIGH”, “LOW”, “LEFT”, “RIGHT”),
DX=0.0,),
_F (GROUP_NO= (“HIGH”, “LOW”, “LEFT”, “RIGHT”),
DY=0.0,),
_F (GROUP_MA=' GAUCHE',
PRE2=15000.,),
_F (GROUP_MA=' GAUCHE',
PRE1=1.E6,),
),
);


SIGINIT=CREA_CHAMP (MAILLAGE=MAIL,
OPERATION=' AFFE',
TYPE_CHAM=' CART_SIEF_R',
AFFE= (_F (GROUP_MA=' BO',
NOM_CMP=
(“SIXX”, “SIYY”, “SIZZ”, “SIXY”, “SIXZ”,
“SIYZ”, “SIP”, “M11”, “FH11X”, “FH11Y”, “ENT11”,
“M12”, “FH12X”, “FH12Y”, “ENT12”,
“QPRIM”, “FHTX”, “FHTY”, “M21”,
“FH21X”, “FH21Y”, “ENT21”,
“M22”, “FH22X”, “FH22Y”, “ENT22”,),
VALE=
(0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 2500000.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0., 0., 0., 0.),),
),);


U0=STAT_NON_LINE (MODELE=MODELE,
CHAM_MATER=CHMAT0,
EXCIT= (
_F (CHARGE=TIMP,),),
COMP_INCR=_F (RELATION=' KIT_THHM',
RELATION_KIT= (“ELAS”, “LIQU_AD_GAZ_VAPE”, “THER_POLY”, “HYDR_UTIL”),),
ETAT_INIT=_F (DEPL=CHAMNO,
SIGM=SIGINIT,),
INCREMENT=_F (LIST_INST=INST1,
),
NEWTON=_F (MATRICE=' TANGENTE',
REAC_ITER=1,),
RECH_LINEAIRE=_F (RESI_LINE_RELA=0.10000000000000001,
ITER_LINE_MAXI=3,),
CONVERGENCE=_F (
RESI_GLOB_RELA=1.E-6,
ITER_GLOB_MAXI=80,
),
PARM_THETA=0.8,
SOLVEUR=_F (METHODE=' MULT_FRONT',
STOP_SINGULIER=' NON',),
);



FIN ();
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Appendix 3 Exemple 2 of command files

# EXAMPLE OF CALCULATION AXIS_THHMD FOR A BI-MATERIAUX (BARRIER OUVRAGEE AND
# BARRIER GEOLOGICAL)

BEGINNING (CODE=_F (NOM=' WTNA100A', NIV_PUB_WEB=' INTERNET'),);


MAIL=LIRE_MAILLAGE ();

#
# LISTS MOMENTS OF CALCULATION
#


INST1=DEFI_LIST_REEL (DEBUT=0.0,
INTERVALLE= (_F (JUSQU_A=1.E7, NOMBRE=10,),
_F (JUSQU_A=1.E8, NOMBRE=1,),
_F (JUSQU_A=1.E9, NOMBRE=9,),),);


MAIL=DEFI_GROUP (reuse =MAIL,
MAILLAGE=MAIL,
CREA_GROUP_NO= (_F (GROUP_MA=' LBABG',),
_F (GROUP_MA=' LBABO',),
_F (GROUP_MA=' LINTBO',),
_F (GROUP_MA=' LINTBG',),
_F (GROUP_MA=' SURFBO',),
_F (GROUP_MA=' SURFBG',),
_F (GROUP_MA=' SURF',),),);

MODELE=AFFE_MODELE (MAILLAGE=MAIL,
AFFE=_F (TOUT=' OUI',
PHENOMENE=' MECANIQUE',
MODELISATION=' AXIS_THHMD',),);
#
#


UN=DEFI_CONSTANTE (VALE=1.0,);

ZERO=DEFI_CONSTANTE (VALE=0.0,);

VISCOLIQ=DEFI_CONSTANTE (VALE=1.E-3,);

VISCOGAZ=DEFI_CONSTANTE (VALE=1.8E-05,);

DVISCOL=DEFI_CONSTANTE (VALE=0.0,);

DVISCOG=DEFI_CONSTANTE (VALE=0.0,);


LI2=DEFI_LIST_REEL (DEBUT=0.0,
INTERVALLE=_F (JUSQU_A=1.E9, PAS=1.E6,),);

LI1=DEFI_LIST_REEL (DEBUT=1.E-5,
INTERVALLE=_F (JUSQU_A=1.0, PAS=0.099999,),);

#
# PROPERTIES OF BARRIER OUVRAGEE
#

LTBO=DEFI_CONSTANTE (VALE=0.59999999999999998,);
LSO = FORMULA (REAL = ''' (REAL:SAT) = (0.35 * SAT) ''');

LSBO=CALC_FONC_INTERP (FONCTION=LSO,
LIST_PARA=LI1,
NOM_PARA=' SAT',
PROL_GAUCHE=' LINEAIRE',
PROL_DROITE=' LINEAIRE',
INFO=2,);
DLSBO=DEFI_CONSTANTE (VALE=0.35,);

SSL = FORMULA (REAL = ''' (REAL:PCAP) = 0.99 * (1.- PCAP * 6.E-9) ''');

SATUBO=CALC_FONC_INTERP (FONCTION=SL,
LIST_PARA=LI2,
NOM_PARA=' PCAP',
PROL_DROITE=' CONSTANT',
PROL_GAUCHE=' CONSTANT',
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INFO=2,);

DSL = FORMULA (REAL = ''' (REAL:PCAP) = - 6.E-9 * 0.99 ''');

DSATBO=CALC_FONC_INTERP (FONCTION=DSL,
LIST_PARA=LI2,
NOM_PARA=' PCAP',
PROL_DROITE=' CONSTANT',
PROL_GAUCHE=' CONSTANT',
INFO=2,);


PERM = FORMULA (REAL = ''' (REAL:SAT) = SAT ''');

PERM11BO=CALC_FONC_INTERP (FONCTION=PERM,
LIST_PARA=LI1,
NOM_PARA=' SAT',
PROL_DROITE=' CONSTANT',
PROL_GAUCHE=' CONSTANT',
INFO=2,);


DPERMBO = FORMULA (REAL = ''' (REAL:SAT) = 1.''');

DPR11BO=CALC_FONC_INTERP (FONCTION=DPERMBO,
LIST_PARA=LI1,
NOM_PARA=' SAT',
PROL_DROITE=' CONSTANT',
PROL_GAUCHE=' CONSTANT',
INFO=2,);


PERM2BO = FORMULA (REAL = ''' (REAL:SAT) = 1.- SAT ''');

PERM21BO=CALC_FONC_INTERP (FONCTION=PERM2BO,
LIST_PARA=LI1,
NOM_PARA=' SAT',
PROL_DROITE=' CONSTANT',
PROL_GAUCHE=' CONSTANT',
INFO=2,);


DPERM2BO = FORMULA (REAL = ''' (REAL:SAT) = - 1.''');

DPR21BO=CALC_FONC_INTERP (FONCTION=DPERM2BO,
LIST_PARA=LI1,
NOM_PARA=' SAT',
PROL_DROITE=' CONSTANT',
PROL_GAUCHE=' CONSTANT',
INFO=2,);
#
# CONDUCTIVITY THERMAL OF THE BO
#


DM8=DEFI_CONSTANTE (VALE=9.9999999999999995E-08,);

KINTBO=DEFI_CONSTANTE (VALE=9.9999999999999995E-21,);

MATERBO=DEFI_MATERIAU (ELAS=_F (E=1.9E+20,
NU=0.20000000000000001,
RHO=2670.0,
ALPHA=0.,),
COMP_THM = “LIQU_GAZ”,
THM_LIQU=_F (RHO=1000.0,
UN_SUR_K=5.0000000000000003E-10,
ALPHA=1.E-4,
CP=4180.0,
VISC=VISCOLIQ,
D_VISC_TEMP=DVISCOL,),
THM_GAZ=_F (MASS_MOL=0.02896,
CP=1000.0,
VISC=VISCOGAZ,
D_VISC_TEMP=ZERO,),
THM_VAPE_GAZ=_F (MASS_MOL=0.017999999999999999,
CP=1870.0,
VISC=VISCOGAZ,
D_VISC_TEMP=ZERO,),
THM_INIT=_F (TEMP=293.0,
PRE1=0.0,
PRE2=1.E5,
PORO=0.34999999999999998,
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PRES_VAPE=2320.0,
DEGR_SATU=0.57420000000000004,),
THM_DIFFU=_F (R_GAZ=8.3149999999999995,
RHO=2670.0,
CP=482.0,
BIOT_COEF=1.0,
SATU_PRES=SATUBO,
D_SATU_PRES=DSATBO,
PESA_X=0.0,
PESA_Y=0.0,
PESA_Z=0.0,
PERM_IN=KINTBO,
PERM_LIQU=PERM11BO,
D_PERM_LIQU_SATU=DPR11BO,
PERM_GAZ=PERM21BO,
D_PERM_SATU_GAZ=DPR21BO,
D_PERM_PRES_GAZ=ZERO,
LAMB_T=LTBO,
LAMB_S=LSBO,
D_LB_S=DLSBO,
LAMB_CT=0.728),);
#
# PROPERTIES OF THE GEOLOGICAL BARRIER
#

KINTBG=DEFI_CONSTANTE (VALE=9.9999999999999998E-20,);

LTBG=DEFI_CONSTANTE (VALE=0.59999999999999998,);
LSG = FORMULA (REAL = ''' (REAL:SAT) =
(0.05 * SAT) ''');

LSBG=CALC_FONC_INTERP (FONCTION=LSG,
LIST_PARA=LI1,
NOM_PARA=' SAT',
PROL_GAUCHE=' LINEAIRE',
PROL_DROITE=' LINEAIRE',
INFO=2,);
DLSBG=DEFI_CONSTANTE (VALE=0.05,);

MATERBG=DEFI_MATERIAU (ELAS=_F (E=1.9E+20,
NU=0.20000000000000001,
RHO=2670.0,
ALPHA=0.0,),
COMP_THM = “LIQU_GAZ”,
THM_LIQU=_F (RHO=1000.0,
UN_SUR_K=5.0000000000000003E-10,
ALPHA=1.E-4,
CP=4180.0,
VISC=VISCOLIQ,
D_VISC_TEMP=DVISCOL,),
THM_GAZ=_F (MASS_MOL=0.02896,
CP=1000.0,
VISC=VISCOGAZ,
D_VISC_TEMP=ZERO,),
THM_VAPE_GAZ=_F (MASS_MOL=0.017999999999999999,
CP=1870.0,
VISC=UN,
D_VISC_TEMP=ZERO,),
THM_INIT=_F (TEMP=293.0,
PRE1=0.0,
PRE2=1.E5,
PORO=0.050000000000000003,
PRES_VAPE=2320.0,
DEGR_SATU=0.81179999999999997,),
THM_DIFFU=_F (R_GAZ=8.3149999999999995,
RHO=2670.0,
CP=706.0,
BIOT_COEF=1.0,
SATU_PRES=SATUBO,
D_SATU_PRES=DSATBO,
PESA_X=0.0,
PESA_Y=0.0,
PESA_Z=0.0,
PERM_IN=KINTBG,
PERM_LIQU=PERM11BO,
D_PERM_LIQU_SATU=DPR11BO,
PERM_GAZ=PERM21BO,
D_PERM_SATU_GAZ=DPR21BO,
D_PERM_PRES_GAZ=ZERO,
LAMB_T=LTBG,
LAMB_S=LSBG,
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Code_Aster ®
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Titrate:
Note of use of model THM


Date:
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:
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D_LB_S=DLSBG,
LAMB_CT=1.539),);

CHMAT0=AFFE_MATERIAU (MAILLAGE=MAIL,
AFFE= (_F (GROUP_MA=' SURFBO',
MATER=MATERBO,),
_F (GROUP_MA=' SURFBG',
MATER=MATERBG,),),);
#
# ASSIGNMENT OF L INITIAL STATE
#

CHAMNO=CREA_CHAMP (MAILLAGE=MAIL,
OPERATION=' AFFE',
TYPE_CHAM=' NOEU_DEPL_R',
AFFE= (_F (TOUT=' OUI',
NOM_CMP=' TEMP',
VALE=0.0,),
_F (GROUP_NO=' SURFBO',
NOM_CMP=' PRE1',
VALE=7.E7,),
_F (GROUP_NO=' SURFBG',
NOM_CMP=' PRE1',
VALE=3.E7,),
_F (NOEUD= (“NO300”, “NO296”),
NOM_CMP=' PRE1',
VALE=5.E7,),
_F (GROUP_NO=' SURFBO',
NOM_CMP=' PRE2',
VALE=0.0,),
_F (GROUP_NO=' SURFBG',
NOM_CMP=' PRE2',
VALE=0.0,),),);
# EVOLUTIONARY FLOW IMPOSES IN INTERNAL P.
#


FLUX=DEFI_FONCTION (NOM_PARA=' INST',
VALE=
(0.0, 386.0,
315360000.0, 312.0,
9460800000.0, 12.6),);

CALEXT=AFFE_CHAR_MECA (MODELE=MODELE,
DDL_IMPO= (_F (TOUT=' OUI',
TEMP=0.0,),
_F (TOUT=' OUI',
PRE2=0.0,),
_F (TOUT=' OUI',
DX=0.0,),
_F (TOUT=' OUI',
DY=0.0,),),);

CALINT=AFFE_CHAR_MECA (MODELE=MODELE,
FLUX_THM_REP=_F (GROUP_MA=' LINTBO',
FLUN=1.0,
FLUN_HYDR1=0.0,
FLUN_HYDR2=0.0,),);

SIGINIT=CREA_CHAMP (MAILLAGE=MAIL,
OPERATION=' AFFE',
TYPE_CHAM=' CART_SIEF_R',
AFFE= (_F (GROUP_MA=' SURFBO',
NOM_CMP=
(“SIXX”, “SIYY”, “SIZZ”, “SIXY”, “SIXZ”, “SIYZ”, “SIP”, “M11”, “FH11X”,

“FH11Y”, “ENT11”, “M12”, “FH12X”, “FH12Y”, “ENT12”, “M21”, “FH21X”, “FH21Y”, “ENT21”, “QPRIM”,
“FHTX”, “FHTY”),
VALE=
(0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, - 70000.0, 0.0, 0.0, 0.0,
2450000.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0),),
_F (GROUP_MA=' SURFBG',
NOM_CMP=
(“SIXX”, “SIYY”, “SIZZ”, “SIXY”, “SIXZ”, “SIYZ”, “SIP”, “M11”, “FH11X”,

“FH11Y”, “ENT11”, “M12”, “FH12X”, “FH12Y”, “ENT12”, “M21”, “FH21X”, “FH21Y”, “ENT21”, “QPRIM”,
“FHTX”, “FHTY”),
VALE=
(0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, - 29900.0, 0.0, 0.0, 0.0,
2450000.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0),),),);

U0=STAT_NON_LINE (MODELE=MODELE,
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Code_Aster ®
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Titrate:
Note of use of model THM


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:
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CHAM_MATER=CHMAT0,
EXCIT= (
_F (CHARGE=CALEXT,),
_F (CHARGE=CALINT,
FONC_MULT=FLUX,),
),
COMP_INCR=_F (RELATION=' KIT_THHM',
RELATION_KIT= (“ELAS”, “LIQU_GAZ”, “THER_POLY”, “HYDR_UTIL”),),
ETAT_INIT=_F (DEPL=CHAMNO,
SIGM=SIGINIT),
INCREMENT=_F (LIST_INST=INST1,),
NEWTON=_F (MATRICE=' TANGENTE',
REAC_ITER=10,),
CONVERGENCE=_F (RESI_GLOB_MAXI=1.0000000000000001E-05,
ITER_GLOB_MAXI=150,
ARRET=' NON',
ITER_INTE_MAXI=5,),
PARM_THETA=0.56999999999999995,
ARCHIVAGE=_F (PAS_ARCH=1,),);

U0=CALC_ELEM (reuse =U0,
MODELE=MODELE,
CHAM_MATER=CHMAT0,
TOUT_ORDRE=' OUI',
OPTION= (“SIEF_ELNO_ELGA”, “VARI_ELNO_ELGA”),
RESULTAT=U0,);

TRB=POST_RELEVE_T (ACTION=_F (INTITULE=' DEPL',
GROUP_NO= (“LBABG”, “LBABO”),
RESULTAT=U0,
NOM_CHAM=' DEPL',
NUME_ORDRE= (1,10,11,20),
NOM_CMP= (“PRE1”),
OPERATION=' EXTRACTION',),);

TRB2=POST_RELEVE_T (ACTION=_F (INTITULE=' CONT',
GROUP_NO= (“LBABG”, “LBABO”),
RESULTAT=U0,
NOM_CHAM=' SIEF_ELNO_ELGA',
TOUT_ORDRE=' OUI',
NOM_CMP= (“M11”, “FH11X”, “FH11Y”),
OPERATION=' EXTRACTION',),);

ZTRB3=POST_RELEVE_T (ACTION=_F (INTITULE=' DEPL',
NOEUD= (“NO294”, “NO295”, “NO299”, “NO300”, “NO304”, “NO305”, “NO309”),
RESULTAT=U0,
NOM_CHAM=' VARI_ELNO_ELGA',
TOUT_ORDRE=' OUI',
NOM_CMP= (“V2”),
OPERATION=' EXTRACTION',),);
IMPR_TABLE (TABLE=TRB,
FICHIER=' RESULTAT',
FORMAT=' AGRAF',
PAGINATION=' INST',
NOM_PARA= (“INST”, “COOR_X”, “PRE1”),);

IMPR_TABLE (TABLE=ZTRB,
FICHIER=' RESULTAT',
FORMAT=' AGRAF',
PAGINATION=' INST',
NOM_PARA= (“INST”, “COOR_X”, “PRE1”),);

#
# V2 density of the liquid
#
IMPR_TABLE (TABLE=ZTRB3,
FICHIER=' RESULTAT',
FORMAT=' AGRAF',
PAGINATION=' INST',
NOM_PARA= (“INST”, “COOR_X”, “V2”),);


FIN ();
Handbook of Utilization
U2.04 booklet: Nonlinear mechanics
HT-66/04/004/A

Code_Aster ®
Version
7.4
Titrate:
Note of use of model THM


Date:
06/07/04
Author (S):
S. GRANET, C. CHAVANT Key
:
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Appendix 4 Post processing GIBI

* FILE DESIGN CONTAINING THE RESULTS
* ---------------------------------------------
OPTI REST FORM “VISUTHMTBTCAS3-1.CAST”;
REST FORM;

* OPTI TRAC PSC;

* trace of the grid
trac TOUT;

* Creation of contours (to be able to trace the isovaleurs
* without the elements: necessary if very fine grid)
contout = contour all;
trac contout;

* list of the moments has to strip
lis0 = lect 0 1 2 3 4 5 6 7 8 9 10;
* model selection
moc = (MAIL ELEM QUA8);
* and (MAIL ELEM SEG3);
*
Mandelevium = MODE moc MECANIQUE ELASTIQUE;


* Looping over the moments
* --------
N = dime lis0;
to repeat loop1 N;
I = (extr lis0 &loop1) + 1;
p = U0. I. inst;
* Deformation
depla = U0. I. DEPL;
titrate “TBT cas3-1: Temps deformation = ' p' seconds”;
def1 = DEFORME TOUT depla 5. red;
init1 = DEFORME TOUT depla 0. blue;
TRAC (def1 and init1);
TRAC def1;
def1s = red DEFORME SABLE depla 1.;
init1s = DEFORME SABLE depla 0. blue;
titrate “TBT cas3-1: Deformation Sable Temps = ' p' seconds”;
TRAC (def1s and init1s);
titrate “TBT cas3-1: Deformation BO Temps = ' p' seconds”;
def1bo = DEFORME (BO1 and BO2) depla 5. red;
init1bo = DEFORME (BO1 and BO2) depla 0. blue;
TRAC (def1bo and init1bo);

* (the chpoint depla is transf in chamelem for the temperatures)
cham2 = CHAN CHAM depla Mandelevium NOEUD;

* Visualization of the temperatures with THM
chtemp = EXCO TEMP cham2;
titrate “TBT cas3-1: Temps temperature = ' p' seconds”;
* trac chtemp Mandelevium 14 TOUT;
trac chtemp Mandelevium 14 contout;
* Visualization of the pressure of pores
chpre1 = EXCO PRE1 cham2;
titrate “TBT cas3-1: Pressure of Temps pores = ' p' seconds”;
* trac chpre1 Mandelevium 14 TOUT;
* Visualization of the increase in gas pressure
chpre2 = EXCO PRE2 cham2;
titrate “TBT cas3-1: Increase in Pgz Temps = ' p' seconds”;
trac chpre2 Mandelevium 14 contout;
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* Constraints
sig = U0. I. SIEF;
sigxx = EXCO SMXX sig;
sigyy = EXCO SMYY sig;
sigzz = EXCO SMZZ sig;
sigp = EXCO SIP sig;
* Calculation forced Totales
sixxt = sigxx + sigp;
siyyt = sigyy + sigp;
sizzt = sigzz + sigp;
TITRATE “TBT CAS3-1: Constraint Sxx Temps = ' p' seconds”;
* trac sigxx Mandelevium 14 TOUT;
trac sigxx Mandelevium 14 contout;
* TITRATE “TBT CAS3-1: Cont. total Sxx Temps = ' p' seconds”;
* trac sixxt Mandelevium 14 contout;
TITRATE “TBT CAS3-1: Constraint Syy Temps = ' p' seconds”;
* trac sigyy Mandelevium 14 TOUT;
trac sigyy Mandelevium 14 contout;
* TITRATE “TBT CAS3-1: Cont. total Syy Temps = ' p' seconds”;
* trac siyyt Mandelevium 14 contout;
TITRATE “TBT CAS3-1: Constraint Szz Temps = ' p' seconds”;
* trac sigzz Mandelevium 14 TOUT;
trac sigzz Mandelevium 14 contout;
* TITRATE “TBT CAS3-1: Cont. total Szz Temps = ' p' seconds”;
* trac sizzt Mandelevium 14 contout;
TITRATE “TBT CAS3-1: Pressure SIP Temps = ' p' seconds”;
trac sigp Mandelevium 14 contout;

* variable internal
VAr = U0. I. VARI;
var1 = EXCO V1 VAr;
var2 = EXCO V2 VAr;
var3 = EXCO V3 VAr;
var4 = EXCO V4 VAr;
TITRATE “TBT CAS3-1: Increase porosity has T = ' p' seconds”;
* trac var1 Mandelevium 14 TOUT;
trac var1 Mandelevium 14 contout;
TITRATE “TBT CAS3-1: Accroissement RhoLiq has T = ' p' seconds”;
* trac var2 Mandelevium 14 TOUT;
trac var2 Mandelevium 14 contout;
TITRATE “TBT CAS3-1: Accroissement Pvp has T = ' p' seconds”;
* trac var3 Mandelevium 14 TOUT;
trac var3 Mandelevium 14 contout;
TITRATE “TBT CAS3-1: Saturation has T = ' p' seconds”;
* trac var4 Mandelevium 14 TOUT;
trac var4 Mandelevium 14 contout;

* One reduces to sand
* sigb=REDU sig sand;
* sigxx = EXCO SMXX sigb;
* TITRATE “TBT CAS3-1:SiXX SABLE t=' p' seconds”;
* trac sigxx Mandelevium 14 SABLE;
end loop1;

opti gift 5;

end;
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Appendix 5 Eléments additional on the conditions with
limits in THM
In what follows one does not take into account the dissolved air (the index lq corresponds then to that of water W) and one
stick to the case unsaturated.
We point out here the choice of the unknown factors of pressure.


Behavior
LIQU_GAZ and LIQU_VAPE_GAZ
PRE1
Capillary pressure: p = p - p
C
gz
lq
PRE2
Gas p pressure =
+
gz
vp
p
not

Variational A5.1 Formulation of the conservation equations

One refers here to [R7.01.11]. These equations are

lq
m + vp
m + Div (Mlq + Mvp) = 0
& &






éq A5.1-1

have
m + Div (Mas) = 0
&









éq A5.1-2

The deduced variational formulation is given by

-

M
M

(m
+ m
D +
+
. D =
lq
vp) 1
(lq
vp)
1
& &


éq
A5.1-3
M
M


(
+
. D
P
lq
vp
ext.
ext.) 1
1
1ad

- m D + Mr. D =

have
2
have
2
&





éq A5.1-4
M
. D
P

have ext.
2
2
2 AD

The capillary pressures and of gas are related to the pressure of water, vapor and dry air by the relations:

PC = pgz - plq








éq A5.1-5

pgz = pvp + not








éq A5.1-6
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Code_Aster ®
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The steam pressure is not an independent variable. It is connected to the pressure of liquid lq
p by
relations

dp
dp
vp
lq
=
+ (hm
m
-
vp
lq) dT
H






éq A5.1-7


T
vp
lq
dp
m
p
=
+ 1 -
lq
dh
C dT
3
T
lq
(
) lq
lq





éq A5.1-8
lq
dhm = C p dT
vp
vp









éq A5.1-9

These relations show that the steam pressure is given completion not the knowledge of lq
p
plq - 0
p

lq
R
p

(and of its evolution). Often, these relations are used to establish the law of Kelvin,

vp

=
T ln
,

ol
sat

lq
Mvp
p (T)
vp

but this law is not used directly in Aster.

The reference documents Aster do not say anything on what are variables 1 and 2. But two elements
can put to us on the track:

· On the one hand, P and P whereas P and P are spaces of membership of PRE1
1
1ad
2
2ad
1ad
2ad
and PRE2 (thus including their boundary conditions).
· In addition, in chapter 7. of [R7.01.10], one sees that the virtual deformation
*
E elg = (v, (v),
is related to the vector of virtual displacement nodal
1,
1,
2,
2,)
*
U el = (v,
by the same operator
el
Q that that which connects between them the deformation
1,
2)
G
el
E = U, U,
and nodal displacement
el
U = (U, p, p, T:
1
2
)
1
,
,
1
2
,
2

G
(() p p p p T T)
-
el
el
*
el
*
E G = Q U
G
-
el
el
el
E = Q U
G
G

It is then clear that and are virtual variations of p and p
1
2
1
2
From where the table:

*
p = p = p
= p
1
C
1
C
C
*
p = p = p
= p
1
lq
1
lq
lq
*
p = p = p

= p
2
gz
2
gz
gz
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A5.2 Cas of boundary conditions utilizing unknown factors
principal

What we say in this paragraph and the following relates to part of the border
D on which
conditions are prescribed: nothing prevents of course that these conditions are not the same ones on
parts of different borders. We treat in this chapter the usual case where one imposes conditions on
PRE1 and/or PRE2, in opposition to the following chapter where we will speak about linear relations between unknown factors.

imp
PC = pgz - plq = p

C
imp
pgz = not + pvp = p

gz

Flows are then computation results by [éq A5.1-3] and [éq A5.1-4]



· Dirichlet PRE1, neuman PRE2

It is the case where one imposes a value on PRE1 and a value with flow associated with PRE2, by not saying anything on PRE2
or by giving a value to FLUN_HYDR2 of FLUX_THM_REP in AFFE_CHAR_MECA. Let us call m2 ext. this
imposed quantity, which will be worth 0 if nothing is known as relative with PRE2. We will note
imp
p
p
1 =
the condition
1
imposed on PRE1
This corresponds to:
imp
PC = pgz - plq = PC
imp
imp
p
= p
1
C

To make the demonstration within the nonhomogeneous framework, it would be necessary to introduce a raising of the condition
imp
p
p
1 =
(c.à.d a particular field checking this condition). That weighs down the writings and does not bring anything, one
1
within the homogeneous framework imp is thus placed
p
= 0
1

In [éq A5.1-3] and [éq A5.1-4], one can thus take and unspecified and checking = 0 on

One
2
1
1
D
then start to take = 0 and = 0 on all the edge
and one obtains [éq A5.1-1] and [éq A5.1-2] with
1
2
feel distributions. One multiplies then [éq A5.1-1] by such as = 0 on

one multiplies [éq A5.1-2]
1
1
D
by unspecified, one integrates by part, one takes account of [éq A5.1-3] and [éq A5.1-4] and one obtains, in
2
indicating by N the normal at the edge:

Mr.
N
M

have
D =
ext. D =

2

D

2
2
2
D
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Note of use of model THM


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One deduces some
Mr. N = M
on

2


have
ext.
D

· Dirichlet PRE2, neuman PRE1

It is the case where one imposes a value on PRE2 and a value with flow associated with PRE1, by not saying anything on PRE1
or by giving a value to FLUN_HYDR1 of FLUX_THM_REP in AFFE_CHAR_MECA. Let us call M1ext this
imposed quantity, which will be worth 0 if nothing is known as relative with PRE2. We will note
imp
p
p
2 =
the condition
2
imposed on PRE2
This corresponds to:
imp
pgz = not + pvp = p gz
imp
imp
p
= p
2
gz

The demonstration is the same one as in the preceding paragraph and leads to:

(M + Mr. N =M on

1


lq
vp)
ext.
D

A5.3 Cas of boundary conditions utilizing relations
linear between principal unknown factors

Code_Aster makes it possible to introduce like boundary conditions of the relations between degrees of freedom, carried
by the same node or different nodes. This possibility is reached via key word LIAISON_DDL of
command AFFE_CHAR_MECA.

That is to say imp
p
the value which one wants to impose on the pressure of liquid on
D. Compte tenu de [éq A5.1-5], and of
lq
choice of the principal unknown factors for this behavior, one writes:

imp
p - p = p






éq A5.3-1
2 - p1 = p
gz
C
lq

The linear relations are treated in Aster by introduction of multipliers of Lagrange. This corresponds
in the species with the following formulation:

To find 1
p, p2, µ such as:

- m
m
D
M
M
D
m
D
M
D
(lq +
vp)
+
lq +
.
vp
-
have
+
.
have
+
1
(
) 1

2

2
& &
&
éq
A5.3-2
+
*
µ p - p - imp
p

D +
-
- imp
p

D

D
(
µ

, µ
2
1
lq)
D (2 1 lq)
*
1
2

To make the demonstration within the nonhomogeneous framework, it would be necessary to introduce a raising of the condition
p - p - imp
p
= 0
2
1
(a.c. D of the particular fields checking this condition). That weighs down the writings and
lq
do not bring anything, one thus places within the homogeneous framework imp
p
= 0
lq
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One then starts to take = 0 and = 0 on all the edge
and one obtains [éq A5.1-1] and [éq A5.1-2] with
1
2
feel distributions. One multiplies then [éq A5.1-1] by unspecified one multiplies [éq A5.1-2] by
1
2
unspecified, one integrates by part, one carries the results found in [éq A5.3-2] and one obtains:


M
M
N D
M N
D
lq +
+
+
(
).
.
1

2
D
have
D
vp
éq
A5.3-3

*
µ p - p
D +
-

D
=


(
µ

0
, µ
2
1)

D

(2 1)
*
1
2
D

It is clear that [éq A5.3-3] p gives again well - p = imp
p
= 0
2
1

lq

While taking moreover - = 0, one find:
2
1


M
M
M
N D

lq +
vp +
have
=

D (
).
0

1
1

From where one deduces:
(M +M +M.N =0
on





éq A5.3-4
lq
vp
have)
D

A5.4 Les nonlinear cases

We do not make here that to tackle more difficult questions consisting in imposing either the steam pressure or
pressure of dry air. Taking into account the relations [éq A5.1-7], [éq A5.1-8] and [éq A5.1-9] to impose a value on
steam pressure amounts imposing a nonlinear relation on the pressure of liquid. In the same way to impose one
pressure of dry air.

As example, we approach the case of a pressure of dry air imposed for a behavior
LIQU_VAPE_GAZ, and we suppose that we can write the nonlinear relation connecting the pressure of
vapor and pressure of liquid.

The relation to be imposed is thus:
imp
p = p - p = p






éq A5.4-1
2 - p
= p
have
gz
vp
vp
have

By differentiating this relation, one will find a condition on the virtual variations of pressures:

p

p

vp
vp
dp = dp -
dp = dp -
dp - dp
have
gz
lq
gz
(gz c)
p

p

lq
lq
That is to say still
p

p


p


dp = dp
vp
-
dp - dp
vp
=
dp + 1
vp
-
dp
have
2
(2
1)
1
2
p

p


p

lq
lq

lq

The variational formulation would be then:

- m
m
D
M
M
D
m
D
M
D
(lq +
vp)
+
lq +
.
vp
-
have
+
.
have
+
1
(
) 1

2

2
& &
&

p

p

imp
vp


+
*
µ

p - p
p
D
D
vp -
+
+ - vp

D
(
µ

1

, µ
2
have)
*
1
2
1
2





p
p
lq





lq

D
Handbook of Utilization
U2.04 booklet: Nonlinear mechanics
HT-66/04/004/A

Code_Aster ®
Version
7.4
Titrate:
Note of use of model THM


Date:
06/07/04
Author (S):
S. GRANET, C. CHAVANT Key
:
U2.04.05-A Page
: 49/50

And one would find:


p

p
vp




M
M
N D
M N
D
D

lq +
+
+
+ - vp
=

(
).
.
µ

1

0
,
1

2
1
2
1
2
D
have
D
vp





p
p
lq





lq

D

p

p
vp


While taking
+ 1 - vp = 0 one would find:
1
2


p
p
lq

lq


p
p
vp

1
(M



éq A5.4-2
lq + M vp) .n -
vp Mr. N
have
= 0


p
p
lq



lq

Handbook of Utilization
U2.04 booklet: Nonlinear mechanics
HT-66/04/004/A

Code_Aster ®
Version
7.4
Titrate:
Note of use of model THM


Date:
06/07/04
Author (S):
S. GRANET, C. CHAVANT Key
:
U2.04.05-A Page
: 50/50

Intentionally white left page.
Handbook of Utilization
U2.04 booklet: Nonlinear mechanics
HT-66/04/004/A

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