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New architecture THM. Integration of the equilibrium equations Date
:

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Author (S):
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:
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: 1/36

Organization (S): EDF-R & D/AMA
Handbook of Descriptif Informatique
D9.05 booklet: -
Document: D9.05.03
New architecture THM. Integration of
equilibrium equations

Summary:

In order to allow the development of rather general nonlinear laws of behavior in the module
THM of Code_Aster, it appeared necessary to completely separate the equilibrium equations and the relations
of behavior.

This document defines the principles of this separation, and described the specifications of under program
credits EQUTHM, integrating one or more equilibrium equations and calling the laws of behavior.
One supposes that the medium can be made up with more than one solid and of two components, each of these two
components being able to exist under two phases. Each one of these elements can or not exist, it thermal can
to be taken into account or not. The thermal equation not takes into account a formulation in entropy, but
in energy utilizing mass enthali of the components.
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New architecture THM. Integration of the equilibrium equations Date
:

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:
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Count

matters

1 variational Writings of the equilibrium equations ................................................................................ 3
1.1 Mechanics ....................................................................................................................................... 3
1.2 Hydraulics ...................................................................................................................................... 3
1.3 Thermics ........................................................................................................................................ 4
2 Laws of behavior ........................................................................................................................... 6
2.1 Mechanics ....................................................................................................................................... 6
2.1.1 General writing .................................................................................................................... 6
2.1.2 Case of the effective constraints ............................................................................................... 6
2.1.3 Choice of the constraints ............................................................................................................. 6
2.2 Hydraulics ...................................................................................................................................... 7
2.3 Thermics ........................................................................................................................................ 7
2.4 homogenized density .................................................................................................... 7
3 generalized Efforts ................................................................................................................................. 7
4 Algorithm of resolution ........................................................................................................................ 8
4.1 Nonlinear algorithm of resolution of the equilibrium equations ..................................................... 8
4.2 Loop on the elements, the points of Gauss ................................................................................. 9
4.3 Vectors and matrices according to options': routine EQUTHM .............................................................. 12
4.3.1 Residue or nodal force: options RAPH_MECA and FULL_MECA ............................................. 13
4.3.2 Loading: options CHAR_MECA ....................................................................................... 14
4.3.3 Tangent operator: options FULL_MECA, RIGI_MECA_TANG ............................................. 14
5 Outlines general ................................................................................................................................. 19
6 Specifications of under generic program EQUTHM ...................................................................... 20
6.1 Arguments of the routine ................................................................................................................. 20
6.2 Addressing in the tables of deformation and constraint .......................................................... 22
6.2.1 Addressing in the deformations ........................................................................................ 22
6.2.1.1 Deformations time less ...................................................................................... 22
6.2.1.2 Deformations time more ......................................................................................... 22
6.2.2 Addressing in the constraints ........................................................................................... 23
6.2.2.1 Constraints time less ......................................................................................... 23
6.2.2.2 Constraints time more ............................................................................................ 23
6.2.3 Addressing in the variables intern (example) ............................................................... 23
6.2.3.1 Variables intern at time less .......................................................................... 23
6.2.3.2 Variables intern at time more ............................................................................. 23
6.3 Addressing R, DRDS, DSDE ............................................................................................................. 24
6.3.1 Addressing in R ................................................................................................................ 24
6.3.2 Addressing in DRDS .......................................................................................................... 24
6.3.3 Addressing in DSDE .......................................................................................................... 25
6.4 Algorithm routine EQUTHM ............................................................................................................ 29
6.5 Arguments of the routine of call of the laws of behavior ......................................................... 33
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New architecture THM. Integration of the equilibrium equations Date
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:
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1
Variational writings of the equilibrium equations

1.1 Mechanics

One leaves the following differential writing:

Div
R m
+ F = 0








éq 1.1-1

We will further see we always adopt the decomposition = + I, where indicates
p
the effective constraint.

It is thus with the load of the module of integration of the equilibrium equations to make the sum:
= + I.
p
One will then write a variational form of [éq 1.1-1] at time T +.

+

= +
+ +

I

p

éq
1.1-2
+
+
m
ext.

+.

(v) = +rF .v +

F
v
v U

AD

1.2 Hydraulics

One leaves the following differential writing:
DM + Div (M) = 0 éq
1.2-1
dt
It is considered that there can be two components, and for each one D `them two phases.

More precisely, the variables m, M and m, M refer each one to a component of mass
1
1
2
2
conservative.

One poses by principle:
m = m1 + m2
1
2
;
M = M + M
1
1
1
1
1
1
m = m1 + m2
1
2
;
M = M + M
2
2
2
2
2
2

What we will write:
m
= mphase
component
component
Nb phasedu
component

phase
M
= M
component
component
Nb phasedu
component

In the applications, one could for example have:

2 components: air and water
2 phases for water
1 phase for the air
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One would have then:
m1 and
1
M: contribution of mass and liquid water flow
1
1

m2 and
2
M: contribution of mass and vapor flow
1
1

m1 and
1
M: contribution of mass and flow of dry air
2
2

m2 and
2
M: non-existent
2
2

It is considered that there are two pressures. No assumption is made on what the pressures mean
p and p, that will depend on the laws of behavior and the way which one will choose to write them: one
1
2
could for example choose:

p = pressioncapillaire (p (gas) - p (liquid))
1

p = pressionde Z
ga (vapor + air)
2

One will write then a variational form of [éq 1.2-1].
D (m1
2
1 + m1)
-
1
2
1
2

M
Mr.
M
M
.

éq
1.2-2
1
(1
1)
1
(1ext
1 ext.)
P


+
+
=
+
1
1
dt
1ad

D (m1 + m2
2
2)
-
2 + (1
2
M2 + m2). 2 =
(1
2
M
+ M
.
P
2ext
2ext)
2
2
2ad éq
1.2-3

dt


After discretization by a teta method:
-

M
M
.
(1+
m
2
1
2


1
+ +
m1) 1 + T (+1 + +1) 1 =
-

M
M
.
éq
1.2-4
(1
m
2
1
2

1

1
+ -
m1) 1 - (-) T (- 1 + - 1) 1
+ T

M
M
.
(
1
2


1
+ 1) 1
1 P
ext.
ext.
has
1 D
-

M
M
.
(1+
m
2
1
2


2
+ +
m2) 2 + T (+2 + +2) 2 =
-

M
M
.
éq
1.2-5
(1
m
2
1
2

1

2
+ -
m2) 2 - (-) T (- 2 + - 2) 2
+ T

M
M
.
(
1
2


2
+ 2) 2
2 P
ext.
ext.
2ad

1.3 Thermics

We introduce the enthali of each phase of each component: H p
C m

We note: Np the number of phases of the component C.
C

We adopt the rule of summation of the dumb indices:

npc
dmp
npc
dmi
HP
p
M =
hi
I
M

HP
C =
hi
C


C m
C
cm
C
C m
dt
C m
I 1
dt
I =1
=
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:
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The equation of thermics (or energy) is written:

dQ'
dmp
+ HP
C + Div p
p
p
m
M + Q = + Mr. F
éq
1.3-1
C m
(hc m c) R
dt
dt
C

One will then write a variational form of [éq 1.3-1] without injecting the hydraulic equilibrium equation there:

dQ'
dmp


HP
C
HP
p
M
Q.
R
p
Mr. F
HP
p
M
Q
.

+
dt
C m

-
+
=
+
-
+
dt
(C m c)
(
C
) (C m cext ext.)







Tad
éq 1.3-2
The discretization of [éq 1.3-2] by teta method leads to:



M
Q
1

M
Q
(Q'+ - Q'-) - T (H p+
p+
+
p
p
-
+
- -
+
+…
C m
C
)
(
) T (hc m C
)
+ hp+ p+
p
p
p+
p
-
+ 1
-
-
=
C


m

(m m
C m
C m)
(
) hc m

(m m
C m
C m)
+ T

p+
m
p
m

p
p
Mr. F + 1 -
Mr. F +
-


M
+
Q
. T
C
(
) T


T
C
R
T


(hc m cext ext.)
AD
éq 1.3-3
One notices in the equation [éq 1.3-3] a term of contribution of heat by the flow of fluid at the edge of

field:
+
.
(H p
p
M
Q
C m
C ext.
ext.)

One will be able in makes consider that the conditions of heat flux define directly:

~q
p
H M p
Q
=
+

ext.
C m
C ext.
ext.

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2 Laws
of
behavior

2.1 Mechanics
2.1.1 Writing
general


+
= +
(+ + + + - - - - - -
, p, p, T;
1
2
, p, p, T,
1
2
,)


éq
2.1.1-1

+
= +
(+ + + + - - - - - -
, p, p, T;
1
2
, p, p, T,
1
2
,)

2.1.2 Case of the effective constraints

In the case of the assumption of the effective constraints, this function will break up in the form:

= + pi

tensor



is
constraint




effective

S
:

scalar

one

is
p
+ = + + + - -
-
-

(, T; , T,)


éq
2.1.2-1
+
= + + + - -
-
-


(, T; , T,)
+
+

=
p+, p+; p, p
-

,
p
p (1 2 1 2 H)


éq
2.1.2-2
+
+
=
p+, p+; p, p
-
,
H
H


(1 2 1 2 H)

It is noticed that in this decomposition:

· the dependence compared to thermics was left in the effective constraints;
typically, it is thought that the laws on the effective constraints are written as in thermo
traditional mechanics:

+ = + (+ - + + -
T;
- - -
T, -
-





,)

· one distinguished the internal variables relating to the law from behavior on the constraints
effective, that one wrote, internal variables of origin hydraulics which one has
written and internal variables of thermal origin which one wrote (see
H
T
following paragraphs).

2.1.3 Choice of the constraints

Because of rather frequent use of the assumption of the effective constraints, one decides that it
vector of the constraints for the mechanical part contains in all the cases the tensor of the constraints
effective and the scalar p. Dans the general case where the assumption of the effective constraints is not
not retained, one will have simply: p = 0.

It is thus with the load of the module of integration of the equilibrium equations to make the sum:
= + I.
p
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2.2 Hydraulics

The hydraulic law of behavior will provide the following relations:

mp+ = mp+ + + + + - - - - Q Q
,
,
,
; ,
,
,
,
, M, _


1
2

1
2

C
C

(p p T p p T Mandelevium D H)

+

, p+,
1
1 p+, p+,
1
2 p+, T +,
2
T+;
it
T pde with npc
p+
p+
M = M


éq 2.2-1
C
C -

, p, p
M
F
1
, p,
1
2 p, T -,
2
T
Q -
_
m+
,
;


D
H


+
+
+
, p+, p+, T+ -
;
1
2
, p, p, T, m, m
=
,
1
2
1
2 _
H
H

(
H)

It is noticed that the field of gravity is a data of the hydraulic law of behavior by it
that the evolution of the vector of flow follows relations of the type: M
=
fl
fl
m
P
.
H
[- + F]

2.3 Thermics

The laws of behavior will provide:

Q'+ = Q'+ (+
, p+, p+, T+; -
1
2
, p, p, T, S -
1
2
)

hp+

= hp+ + + + + - - - - Q
;
1
1
2
, -
1
2


C m
C m (
p p T
p p T sd m)
this pde with npc
+
+
Q = Q (+
, p+, p+, T+, T+
Q
1
2
; -
, p, p, T,
1
2
T, -)

éq 2.3-1
+
+
+
=

(, p+, p+, T+, T+ -
; , p, p, T,
1
2
T
-
, T)
T
T
1
2
With hq-
1
2
1
2
=
,
,
,
D m
(H H H H
1 m
1 m
2m
2 m)

2.4
homogenized density

r+
R
m1+ m2+ m1+ m2+
= 0 + 1 + 1 + 2 + 2
éq
2.4-1

3 Efforts
generalized

It arises of what is written higher than the generalized constraints are:

;
p
m1, 1
M, h1; m2, 2
M, H2;
1
1
1 m
1
1
1 m

m1, 1
M, h1; m2, 2
M, H2;
2
2
2m
2
2
2 m
Q', Q

The associated generalized deformations are:

U, (U); p, p; p, p; T, T
1
1
2
2

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4
Algorithm of resolution

4.1
Nonlinear algorithm of resolution of the equilibrium equations

In the general case of modeling (variable coefficients, desaturation, convection) the problem
variational presented above is nonlinear compared to the fields of displacement, pressure and
temperature. After discretization by finite elements, one obtains a nonlinear matric system.
stamp resolution contains moreover one nonsymmetrical term and is treated like such (not
symmetrization of this matrix to use methods of minimum). One uses in all the cases of
modeling the nonlinear solvor of Code_Aster STAT_NON_LINE resting on a method of
Newton-Raphson, described in [R5.03.01]. Its principle is as follows (the equations corresponding to
processing by dualisation of the boundary conditions are not indicated explicitly here).

The equilibrium equation thermo poro-mechanics at the moment T +, knowing at the previous moment
(U, -

P, -

T), as well as the possible internal variables is written:

F (U, P
, T
+
=
-
+
+
+)
L (T) G (U, P
, T
,
I
E
-
-
-)

To find the solution of this nonlinear equation, a continuation is built:

· initialized by a prediction which gives (U, P, T) = (U, P, T
- - -) + (U
0
0
0
0, 0
P, 0
T):

DF
+
-
(
· U
,
0
,
0
0 =
-
U
-
-)
,
(
P
T) L (T) L (T
I
P
T
E
E
)

· corrected by recurrence giving (U, P, T
,

,
,
:
1
1
1 =
+
+
+
+)
(U P T) (U P T
N
N
N
N
N
N
n+1
n+1
n+1)

DF ·(U,
,
,
,
1 P 1 T
+
+
+
+1) = - F (U
P T) + L (T) - G (U P T
I
N
N
N
I
N
N
N
E
-
-
-)

The following notations were adopted:

·
F (U, P
, T
contains the work of deformation, the contributions to the current moment of the terms
I
)
of hydraulic and thermal dissipation expressed within - method, and of the variations
of fluid contribution of mass and entropy;
·
DF appoints the tangent operator, who can not be brought up to date with each iteration in
I
(U, P, T, according to a compromise cost calculation-speed of convergence; convergence is
N
N
N)
checked by a test on the relative standard of the difference of reiterated successive (via the key word
INCO_GLOB_RELA);
·
G (U, P
, T
-
-
-
) contains the contributions to the previous moment of the terms of dissipation
hydraulics and thermics expressed within - method, and of the variations of contribution of
mass fluid and of entropy;
·
L (T indicates the virtual work of the “dead” forces external and external contributions
E
)
hydraulics and of heat expressed by - method.

With convergence with the iteration
N +1, one operates an updating of the fields
(U, P, T) = (U
+
+
+
+,
P
1
+, T
N
N 1
n+
1).
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In the version present of algorithm THM, we decided to gather all the terms y
included/understood those due to the following forces and those of time less:

While posing:

- R (U, P, T) = - F (U, P, T) - G (U, -
P, -
T
=
I
N
N
N
I
N
N
N
), therefore DF DR.
I
I

one has finally:

DF ·(U, P, T
+

,
1
1
+
+
+1) = - R (U
P T) + L (T
I
N
N
N
I
N
N
N
E
)

The general algorithm of balance will be written then, for a step of time:

Initializations:
Calculation of L (t+ (option
E
)
CHAR_MECA)
Calculation of DF
(option
I (U P T
RIGI_MECA-TANG)
-
-
-)
,
Calculation of (U,
P,
T by: DF
· U
, P


0
, T

0
0 = L t+ - L T
0
0 0)
I (U P T
-
-
-)
,
(
) E () E ()

Iterations of balance of Newton N
If option FULL_MECA:
Calculation of DF
and - (+ + +
R U, P, T:
I
N
N
N)
I (u+, P+, T+
N
N
N)
update stamps tangent: DF = DF

I
I (+, P+, T+
N N)
If option RAPH_MECA
Calculation of - (+ + +
R U, P, T
I
N
N
N)
Calculation of (U, P, T
by:
n+1 n+1 n+1)
DF ·(U, P, T
+
+
+
+

,
,

1
1
+
+
+1) = - R (U P T) + L (T
I
N
N
N
I
N
N
N
E
)
Updating:
(u+, P+, T+
+
+
+
,
,

,
,

1
1
1 =
+
+
+
+)
(U P T) (U P T
N
N
N
N
N
N
n+1
n+1
n+1)
IF test convergence OK
end Newton: no next time
If not
N = n+1

4.2
Loop on the elements, the points of Gauss

As in all the codes of finite elements, the terms are calculated by loop on the elements and
loop on the points of gauss:

R
+
+
+
el
el
U,
,

u+
+
+
=
,
,
I (
P T
N
N
N)
W R
G
G I (
P T
N
N
N)
el
G

DF
el
el
+
+
+
=
,
,

I (U P T
+
+
+
N
N
N)
W DF
G
G I (U, P, T
N
N
N)
el
G
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Let us note: {X el} the vector of the nodal unknown factors, on a finite element el

U
v
W
1

node
p1
p
2
T
U
v
W
for example

{Xel} =
2

node
p1
p
2
T
U
v
W
3

node
p1
p

2
T

In this paragraph, to simplify the presentation, we suppose that we deal with one
supporting finite element of the ddl of displacement, two ddl of pressure and a ddl of temperature.

Let us note {el the vector of the deformations generalized at the point of gauss G of the element el
G}
For example:

U
(U)


p
1
{
p

1
el
=

G}


p
2
p

2
T


T


We note {el the vector of constraints generalized for the point of Gauss G of the element el
G}
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For example, and always in the most complete case:




p


m1
11
M1
h1
1 m
2
m
1
2
M
1
{
H2

1

el
m
=
G}
1
m
2
1
M
2
1
H
2m
m2
2
2
M2
H2
2 m


Q'


Q

el
The routines finite elements calculate the matrix: [B] defined by:
G

{el
el
= B
X
G}
[] G {}
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New architecture THM. Integration of the equilibrium equations Date
:

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Author (S):
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:
D9.05.03-A Page
: 12/36

The algorithm will become then:

Initializations:
Calculation of L (t+ (option
E
)
CHAR_MECA)
Calculation of DF
(option
I (U P T
RIGI_MECA-TANG)
-
-
-)
,
Calculation of (U,
P,
T by: DF
· U
, P


0
, T

0
0 = L t+ - L T
0
0 0)
I (U P T
-
-
-)
,
(
) E () E ()
Iterations of balance of Newton N
Loop elements el
Loop points of gauss G
el
calculation [B]
G
-
el
+
el
calculation {el
B
X -
=
and {el
B
X +
=

G N} [] G {N}
G} [] G {
}
el
Calculation +
el
+
+
+
el
G, - R (U, P, T
and DF
(according to options) from:
I G
N
N
N)

N
G I (u+, P+, T+
N
N
N)
{el- el+ el- el+ el
,
,
,
, B
G} {G N} {G} {G N} [] G
Calculation of (U, P, T
by:
n+1 n+1 n+1)
DF ·(U, P, T
+
+
+
+

,
,

1
1
+
+
+1) = - R (U P T) + L (T
I
N
N
N
I
N
N
N
E
)
Updating:
(u+, P+, T+
+
+
+
,
,

,
,

1
1
1 =
+
+
+
+)
(U P T) (U P T
N
N
N
N
N
N
n+1
n+1
n+1)
IF test convergence OK
end Newton: no next time
If not
N = n+1

4.3
Vectors and matrices according to options': routine EQUTHM

The framed central part of the algorithm presented Ci above is carried out by a generic routine
EQUTHM. We give in appendix a chart of the call of this routine.

This routine is parameterized according to the equations present (mechanics, hydraulics with 1 or
2 pressures, thermics). The work carried out by this routine is parameterized by the option.

The term - R (U, P, T will be calculated by the options
I
N
N
N)
RAPH_MECA and FULL_MECA. This term includes them
following forces of volume: it will be considered that the following forces will be integrated into the options
RAPH_MECA, FULL_MECA and RIGI_MECA_TANG. If the user data
do not comprise forces of volume, the Fm+ vector will be simply null.

The presentations made in the two following paragraphs are made in the most general case where
there is an equation of mechanics, two equations of hydraulics and an equation of thermics.
routine EQUTHM will calculate or not the various terms according to description that one will make him
equations present.

The indices G and el from now on are omitted, but it is clear that what is described applies to each point
of gauss of each element.
Handbook of Descriptif Informatique
D9.05 booklet: -
HT-66/05/003/A

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:
D9.05.03-A Page
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4.3.1 Residue or nodal force: options RAPH_MECA and FULL_MECA

One will distribute the terms of the variational formulation according to the following principle:

el
el T
If * G indicates a virtual field of deformation, * G = (v, (v),
calculated
1,
1,
2,
2,)
starting from a vector of displacement nodal virtual: {X el *}
* elT
el
G. R
U
P T = R v







1
+ R v
2
+ R3 1 + R4 1 + R5 2 + R6 2 + R7 + R8
I G (
,
,
+
+
+)
()

One has then:

Index R
associated

+
+
+

1
+
1
2
1
2
-
+
m
v
1
+ m1 + m2 + 2 m
m
F





2
+
+
+ I
(v)
p


3
- 1+ - 2+
1
2

1
+ -
1
+
-
m
m
m
m
1
1
1


4
T (M1+ M2+
1
2
1
-
+
+ -
+


1)
() T (M
M
1
1
1)
1

5
- 1+ - 2+
1
2
2
2
+ -
2
+
-
m
m
m
m
2
2


6
T (M1+ M2+
1 -
2
1
-
+
+ -
+


2) (
) T (M
M
2
2
2)
2


7
Q'+ - Q'-


(h1+
1
1+
1
2+
2
2+
2

1
1
1
+ - 1
1
- 1 + 1 + - 1
1
-
m
(
) H m) (m m) (H m () H m) (m m1)
(

h1+
1
1+
1
2+
2
2+
2

1
1
2
+ - 2
2
- 2 + 2 + - 2
2
-
m
(
) H m) (m m) (H m () H m) (m m2)
- T
(1 +
2 +
1 +
2 +
1
2
1
M
M
M
M
F
1
M
(
M
M
M2 - .Fm
2
)
1
+ 1 + 2 + 2) m
.
- T (-)
-
-
-
1
+ 1 + 2 +


8
- T (1+ 1+
H
2
2
1
1
2
2
M
M
M
M
Q

1
1 +
+
+
h1
1
+ +
+
H2
2
+ +
+
H2
2
+ +
m
m
m
m
) +
- (-) T (1 - 1
H
2
2
1
1
2
2
1
M
M
M
M
Q
1
1 +
-
-
h1
1
+ -
-
H2
2
+ -
-
H2
2
+ -
m
m
m
m
)

From there one will define the vector nodal residue {Vel such as:
G}
{T
X el
*}.{Vel =

G}
el T
*
el
G. R
U,
I G (
P T
+
+
+)

{Vel will be calculated by:
G}
{Vel} = [Beautiful T.R
G
G] {}
Handbook of Descriptif Informatique
D9.05 booklet: -
HT-66/05/003/A

Code_Aster ®
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:
D9.05.03-A Page
: 14/36

4.3.2 Loading: options CHAR_MECA

This chapter is here only for memory because routine EQUTHM will not deal with these terms.

One will distribute the terms of the variational formulation according to the following principle:

* elT
el
+
G. L
T
= L v
v






1
+ L2
+ L3 1 + L4 + L5 2 + L6 2 + L7 + L8
E G ()
()

Index
L
element type associated with
1
F ext+
edge
v


3
T (M1 m2
+
edge



1
1ext
1 ext.)
5
T (M1 m2
+
edge



2
2 ext.
2 ext.)
7
tR
volume





edge
- T (

1

1
2
2
Q +
M
1
1
+
M
ext.
(H
H
m
ext.
1 m
1 ext.)
- T (H 1 1
M
2
2
2
2
+ H

M
m
ext.
2 m
2ext)
= - t~q
ext.

4.3.3 Tangent operator: options FULL_MECA, RIGI_MECA_TANG

Notice on the matric notations:

In what follows, if X indicates a vector of components X I and Y a vector of components
X
X I
Y J,
line:I, column: J is
.

Y will indicate a matrix of which the element (
) Yj

To calculate tangent operator DF, the following quantities will be calculated:
I

[DRDE] =
DR1U DR1E DR1P1 DR1GP1
DR1P2 DR1GP2
DR1T DR1GT
DR2U DR. 2nd DR2P1 DR2GP1
DR2P2 DR2GP2
DR2T DR2GT
DR3U DR. 3rd DR3P1 DR3GP1
DR3P2 DR3GP2
DR3T DR3GT
DR4U DR. 4th DR4P1 DR4GP1
DR4P2 DR4GP2
DR4T DR4GT
DR5U DR. 5th DR5P1 DR5GP1
DR5P2 DR5GP2
DR5T DR5GT
DR6U DR. 6th DR6P1 DR6GP1
DR6P2 DR6GP2
DR6T DR6GT
DR7U DR. 7th DR7P1 DR7GP1
DR7P2 DR7GP2
DR7T DR7GT
DR8U DR. 8th DR8P1 DR8GP1
DR8P2 DR8GP2
DR8T DR8GT

Handbook of Descriptif Informatique
D9.05 booklet: -
HT-66/05/003/A

Code_Aster ®
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New architecture THM. Integration of the equilibrium equations Date
:

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:
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: 15/36

Where one noted:
F

DRiU
I
= U
F

DRiE
I
=
F

DRiP
I
1 = p
1
F

DRiP
I
2 = p
2
F

DRiGP
I
1 =
p1
F

DRiGP
I
2 =
p2
F

DRiT
I
= T

F

DRiGT
I
=


T
Handbook of Descriptif Informatique
D9.05 booklet: -
HT-66/05/003/A

Code_Aster ®
Version
7.4
Titrate:
New architecture THM. Integration of the equilibrium equations Date
:

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Author (S):
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:
D9.05.03-A Page
: 16/36

To make these calculations one considers that the laws of behavior will provide, for the options
corresponding, all the derivative following:




U

p

1
p1 p2

p2
T
T



p
p
p
p
p
p
p
p



U

p

1
p1 p2

p2
T
T

m1
1
1
1
1
1
1
1

1
m1
m1
m1
m1
m1
m1
m1



U

p

1
p1 p2

p2
T
T

M1
1
M1
M1 M1 M1 M1 M1
1
M1 1
1
1
1
1
1



U

p
p
p
p
T
T

1
1
2
2

1
1
1
1
1
1
1
1

H
H
H
H
H
H
H
H

1 m
1 m
1 m
1 m
1 m
1 m
1 m
1 m



U

p
p
p
p
T
T


1
1
2
2

2
2
2
2
2
2
2

m
m
m
m
m
m
m
m2
1
1
1
1
1
1
1
1

U

p
p
p
p
T
T
1
1
2
2


2
2
2
2
2
2
2
2

M
M
M
M
M
M
M
M
1
1
1
1
1
1
1
1


U

p
p
p
p
T
T
1
1
2
2

2
2
2
2
2
2
2
2


H
H
H
H
H
H
H
H
1

m
1 m
1 m
1 m
1 m
1 m
1 m
1 m


U

p
p
p
p
T
T
[
1
1
2
2
DSDE] =
1
1
1
1
1
m
m
m
m
m
1
1
1
m
m
m

2
2
2
2
2
2
2
2



U

p
p
p
p
T
T

1
1
2
2

1
1
1
1
1
1
1
1

M
M
M
M
M
M
M
M

2
2
2
2
2
2
2
2



U

p
p
p
p
T
T


1
1
2
2

1
1
1
1
1
1
1
1

H
H
H
H
H
H
H
H

2m
2m
2m
2m
2m
2m
2m
2m



U

p
p
p
p
T
T

1
1
2
2


2
2
2

m
m
m
m2
2
2
2
2

2
m2
m2
m2
m
2
2
2
2

U

p




1
p1 p2
p2
T
T



2
2
2
2
2
2
2
2
M
M
M
M
M
M
M
M
2
2 2 2 2 2 2 2

U

p




1
p1 p2 p2
T
T

H2
2
2
2
2
2
2
2

2
H2
H2
H2
H2
H2
H2
H
m
m
m
m
m
m
m
2 m



U

p


T
1
p1 p2 p2
T


Q'
Q'
Q'
Q'
Q'
Q'
Q'
Q'



U

p1 p1 p2

p2
T


T


Q
Q
Q
Q
Q
Q
Q
Q


U

p

1
p1 p2

p2
T


T



Handbook of Descriptif Informatique
D9.05 booklet: -
HT-66/05/003/A

Code_Aster ®
Version
7.4
Titrate:
New architecture THM. Integration of the equilibrium equations Date
:

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Author (S):
C. CHAVANT Key
:
D9.05.03-A Page
: 17/36

In fact, in these expressions, the derivative compared to U are all null, but we keep
el
the writing taking into account the definition of the matrices [B] which we adopted.
G

The call to the laws of behavior will provide the pieces of matrix [DSDE] according to equations'
present:










[


p
p
p
p


1 1
2
DMECDE] =
;
[DMECP] 1 =


;
[DMECP2] =


2
[DMECDT] = T

T
p
p
p
p
p
p
p



p1

p1

p2 p2

T T
m1
1
1
1
1


m1
1
1
m1
1
m1
m
1
m1
m1






p


1

p1
p2 p

2


T
T
1


1
1
1
1

1
1
[
M


M
1 M
1
M1 M1
M
1 M
DP11DE] =
;
[
]
DP11P1 =
;
[DP
]
11P2
1

[DP11DT]
1

=

=
p
T
T
1

p1
p2 p

2


h1


1
1
1
1
h1
1
1
H
1m
h1
H
1
m
1 m
h1
H
m
1 m

m
m

p


T
T
1

p1
p2 p2

m2
2
2
2
2


m2
2
1
m1
1
m1
m
1
m1
m1






p


1

p1
p2 p

2


T
T
2


2
2
2
2

2
2
[
M


M1 M
1
M1 M1
M
1 M
DP12DE] =
;
[DP
]
12P1 =
;
[DP
]
12P2
1
[DP12DT]
1


=

=
p


T
T
1

p1
p2 p

2
H2



2
2

2
2
H2
2
1
H
1 m
h1
H
1
m
1 m
h1
H
m
1 m

m
m


p


T
T
1
p1
p2
p2
m1
1
1
1
1


m1
1
2
m2
2
m2
m
2
m2
m2






p


1

p1
p2
p

2


T
T
1


1
1
1
1

1
1
[
M


M2 M
2
M2 M2
M2 M
DP21DE] =
;
[DP
]
21P1 =
;
[DP
]
21P2 =
2

[DP21DT] =
2

p
T
T
1
p1
p2
p

2
h1



1
1

1
1
h1
1
2
H
2m
H2
H
m
2m
H2
H
m
2m

m
2m

p


T
T
1
p
1
p2
p2
m2
2
2
2
2


m2
2
2
m2
2
m2
m
2
m2
m2






p


1

p1
p2
p

2


T
T
2


2
2
2
2

2
2
[
M


M2 M
2
M2 M2
M2 M
DP22DE] =
;
[DP
]
22P1 =
;
[DP
]
22P2 =
2

[DP22DT] =
2

p
T
T
1
p1
p2
p

2
H2



2
2

2
2
H2
2
2
H
2 m
H2
H
m
2 m
H2
H
m
2 m

m
2 m

p


T
T
1
p
1
p2
p2
Q
'
Q
'
Q
'
Q
'
Q
'
Q
'
Q
'
[

DTDE]

=
p

1 p
p
1
2 p


;
[
]

DTDP1


=
;
[DTDP2]



=
2
[DTDT]

T


=
T
Q
Q
Q
Q
Q
Q
Q

p
1

p


1
p
2

p

2
T


T
Handbook of Descriptif Informatique
D9.05 booklet: -
HT-66/05/003/A

Code_Aster ®
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Titrate:
New architecture THM. Integration of the equilibrium equations Date
:

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Author (S):
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:
D9.05.03-A Page
: 18/36

In addition, by deriving the expression from the residue compared to the constraints, one defines:

1
R
1
R
1
R
1
R
1
R
1
R
1
R
1
R
1
R
1
R
1
R
1
R
1
R
1
R
1
R
1
R


1
1
1
2
2
2
1
1
1
2
2
2


p m
M
H
m
H
m
H
m
H
Q'
1
1 1

M
m
1
1 1

M
m
2
2 2

M
m
2
2

Q

2 m

R2 R2
R2 R2
R2
R2
R2
R2
R2 R2
R2
R2
R2
R2
R2 R2


1
1
1
2
2
2
1
1
1
2
2
2


p m
M
H
m
H
m
H
m
H
Q'
1
1 1

M
m
1
1 1

M
m
2
2 2

M
m
2
2

Q

2 m

3
R
3
R
3
R
3
R
3
R
3
R
3
R
3
R
3
R
3
R
3
R
3
R
3
R
3
R
3
R
3
R


1
1
1
2
2
2
1
1
1
2
2
2


p m
M
H
m
H
m
H
m
H
Q'
1
1 1

M
m
1
1 1

M
m
2
2 2

M
m
2
2

Q

2 m

R4
R4 R4 R4
R4
R4
R4
R4
R4 R4
R4
R4
R4
R4
R4 R4


1
1
1
2
2
2
1
1
1
2
2
2

[


p m
H
m
H
m
H
m
H
Q'
1
1 1

m
1
1 1

m
2
2 2

m
2
2


DRDS]


M
M
M
M
Q
2 m

= 5R 5R 5R 5R 5R 5R 5R
v
5
R
5
R
5
R
5
R
5
R
5
R
5
R
5
R


1
1
1
2
2
2
1
1
1
2
2
2




p m
M
H
m
H
m
H
m
H
Q'
1
1 1

M
m
1
1 1

M
m
2
2 2

M
m
2
2

Q

2 m

R6
6
R
6
R
6
R
6
R
6
R
6
R
6
R
6
R
R6
R6
6
R
6
R
6
R
R 6.6
R


1
1
1
2
2
2
1
1
1
2
2
2




p m
M
H
m
H
m
H
m
H
Q'
1
1 1

M
m
1
1 1

M
m
2
2 2

M
m
2
2

Q

2 m

R7
R7 R7 R7
R7
7
R
7
R
7
R
7
R
R7
7
R
R7
R7
R7
7
R
7
R


1
1
1
2
2
2
1
1
1
2
2
2


p m
H
m
H
m
H
m
H
Q'
1
1 1

m
1
1 1

m
2
2 2

m
2
2



M
M
M
M
Q
2 m

8
R
8
R
8
R
8
R
8
R
8
R
8
R
8
R
8
R
8
R
8
R
8
R
8
R
8
R
8
R
8
R


1
1
1
2
2
2
1
1
1
2
2
2


p m
M
H
m
H
m
H
m
H
Q'
1
1 1

M
m
1
1 1

M
m
2
2 2

M
m
2
2

Q

2 m


All these quantities not being inevitably calculated, one will note:






[DR1DS]






=
1
R
1
R
R
R
R
R
R
;
[
]
DR1P11 =
1
1 or
1
1
1

+
+




+
+
1
1

+
+
1
1
p
m

M
m
M
+
1



1
1


1
1
1
m
R1
R
R
R
R
[
1
1
1

DR.
]
1P12 =
1

2+
2+ or
2+
2+
2+
m1
M1
m1
M



1
h1 m
R1
R
R
R
R
[
1
1
1

DR.
]
1P21 =
1

1+
1 + or
1+
1 +
1+
m2
M2
m2
M



2
H2 m
R1
R
R
R
R
[
1
1
1

DR.
]
1P22 =
1

2+
2+ or
2+
2+
2+
m2
M2
m2
M



2
H2 m
[
1
R
R
DR1DT]

=
1


+
+
Q'
Q


In the same way:

[DR8DS], [
]
DR8P11 [
,
]
DR8P12, [D
]
R8P21, [DR8P2]
2, [DR8DT]

It is then clear that:

[DRDE] = [DRDS].[DSDE]

And the contribution of the point of gauss to tangent matrix DF el
is obtained by:
G I (u+, P+, T+
N
N
N)
DFel

el T
el
.
.

I


(u+, P+, T+
G
N
N
N)
[B] [DRDE] [B
G
]

=
G
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5 Diagrams
General

STAT_NON_LINE

finite element

Routine YOU…

Routine EQUTHM
Comp méca

Knows unknown:
Arg In:
Comp hydrau

· T, P1, P 2, U
nature unknown factors
Comp ther

Cal behavior

Loop points of gauss

'
;
p

Calculate deformations:

1
1
1
Assemble contibution
m, M, H
;
1
1 1m

(U),

not gauss with residue
2
m, m2, 2
H
;
1
1
1m
p, p,
1
2 p,
1 p,
2
and/or M tgte
1
T, T
m, M1, 1
H
;
2
2
2m
2
m, m2, 2
H
;
2
2
2m
Calculate [B] elg
'
Q, Q
Cal EQUTHM
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6
Specifications of under generic program EQUTHM

6.1
Arguments of the routine

ARGUMENTS Of INPUT: IN
COMPOR
Description of the behavior
OPTION
Option to be calculated

NDIM
dimension spaces
2 or 3
NDDL
Numbers total degrees of
freedom of the appealing element
DIMDEF
dimension of the table of
deformations generalized with
not gauss
DIMCON
dimension of the table of
constraints generalized with
not gauss
NVIMEC
A number of internal variables
“mechanical”
ADVIME
Address variables

mechanical interns in
table of the internal variables
at the point of gauss
NVIHY
A number of internal variables
“hydraulic”
ADVIHY
Address variables

hydraulic interns in
table of the internal variables
at the point of gauss
NVITM
A number of internal variables
“thermal”
ADVITM
Address variables

thermal interns in
table of the internal variables
at the point of gauss
B (1:dimdef, 1:nddl)
el

Stamp [B]
G
DEFGEP (1:dimdef)
Values of deformations

generalized at the point of
gauss time more
DEFGEM (1:dimdef)
Values of deformations

generalized at the point of
gauss time less
CONGEM (1:dimcon)
Values of constraints

generalized at the point of
gauss time less
VINTM (1:nvimec+nvihy+
Values of the internal variables
nvitm)
at the point of gauss time
less
MECA (1:5)
YAMEC = MECA (1)
logic if 1 there is an equation of
mechanics

ADDEME = MECA (2)
Address in the tables of
deformations at the point of gauss
DEFGEP and DEFGEM of the deformations
corresponding to mechanics

ADCOME = MECA (3)
Address in the tables of
constraints at the point of gauss CONGEP
and
CONGEM of the constraints
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corresponding to the equation ieq

NDEFME = MECA (4)
A number of mechanical deformations

NCONME = MECA (5)
A number of mechanical constraints
PRESS1 (1:5)
YAP1 = PRESS1 (1)
logic if 1 there is an equation
constituting 1

NBPHA1 = PRESS1 (2)
a number of phases for the component

1

ADDEP1 = PRESS1 (3)
Address in the tables of
deformations at the point of gauss
DEFGEP and DEFGEM of the deformations
corresponding to the first pressure

ADCP11 = PRESS1 (4)
Address in the tables of
constraints at the point of gauss CONGEP
and
CONGEM of the constraints
corresponding to the first phase of
first component

ADCP12 = PRESS1 (5)
Address in the tables of
constraints at the point of gauss CONGEP
and
CONGEM of the constraints
corresponding to the second phase
first component

NDEFP1 = PRESS1 (6)
A number of deformations pressure 1

NCONP1 = PRESS1 (7)
A number of constraints for each
phase of component 1
PRESS2 (1:5)
YAP2 = PRESS2 (1)
logic if 1 there is an equation
constituting 2

NBPHA2 = PRESS2 (2)
a number of phases for the component
2

ADDEP2 = PRESS2 (3)
Address in the tables of
deformations at the point of gauss
DEFGEP and DEFGEM of the deformations
correspondent with PRE2

ADCP21 = PRESS2 (4)
Address in the tables of
constraints at the point of gauss CONGEP
and
CONGEM of the constraints
corresponding to the first phase of
second component

ADCP22 = PRESS2 (5)
Address in the tables of
constraints at the point of gauss CONGEP
and
CONGEM of the constraints
corresponding to the second phase
second component

NDEFP2 = PRESS2 (6)
A number of deformations pressure 2

NCONP2 = PRESS2 (7)
A number of constraints for each
phase of component 2
TEMPE (1:5)
YATE = TEMPLE (1)
logic if 1 there is an equation of
thermics

ADDETE = TEMPLE (2)
Address in the tables of
deformations at the point of gauss
DEFGEP and DEFGEM of the deformations
corresponding to thermics

ADCOTE = TEMPLE (3)
Address in the tables of

constraints at the point of gauss CONGEP

and first CONGEM of the constraints

corresponding to thermics

NDEFT = TEMPLE (4)
A thermal number of deformations

NCONT = TEMPLE (5)
A number of thermal stresses

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ARGUMENTS OF OUTPUT: OUT
CONGEP (1:dimcon)
Values of constraints

generalized at the point of
gauss time more
VINTP (1:nvimec+nvihy+
Values of the internal variables
nvitm)
at the point of gauss time more
V (1:nddl)
{

Vel} = [Beautiful T.R
G
G] {}
MAT (1:nddl, 1:nddl)

DF

el

el T
el
.
.
I


(u+, P+, T+
G
N
N
N)
[B] [DRDE] [B
G
]

=
G
TABLES OF WORK
R (1:dimdef)


DRDS


(1:dimdef, 1:dimcon)
DSDE


(1:dimcon, 1:dimdef)

6.2
Addressing in the tables of deformation and constraint

6.2.1 Addressing in the deformations
6.2.1.1 Deformations time less

Part
Significance
Address in DEFGEM
(local name in routine
COMTHM)
DEMECM
U, (U)
ADDEME
DEP1M
p, p
ADDEP1
1
1
DEP2M
p, p
ADDEP2
2
2
DETM
T, T
ADDETE

6.2.1.2 Deformations time more
Part
Significance
Address in DEFGEP
(local name in routine
COMTHM)
DEMECP
U, (U)
ADDEME
DEP1P
p, p
ADDEP1
1
1
DEP2P
p, p
ADDEP2
2
2
DETP
T, T
ADDETE

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6.2.2 Addressing in the constraints

6.2.2.1 Constraints time less

Part
Significance
Address in CONGEM
(local name in routine
COMTHM)
COMECM
,
ADCOME
p
CP11M
m1
1
M
m1
1
or
M h1
,
,
,

ADCP11
1
1
1
1
1 m
CP12M
m2
2
M
m2
2
or
M H2
,
,
,

ADCP12
1
1
1
1
1 m
CP21M
m1
1
M
m1
1
or
M h1
,
,
,

ADCP21
2
2
2
2
2m
CP22M
m2
2
M
m2
2
or
M H2
,
,
,

ADCP22
2
2
2
2
2 m
COTM
Q', Q
ADCOTE

6.2.2.2 Constraints time more
Part
Significance
Address in CONGEP
(local name in routine
COMTHM)
COMECP
,
ADCOME
p
CP11P
m1
1
M
m1
1
or
M h1
,
,
,

ADCP11
1
1
1
1
1 m
CP12P
m2
2
M
m2
2
or
M H2
,
,
,

ADCP12
1
1
1
1
1 m
CP21P
m1
1
M
m1
1
or
M h1
,
,
,

ADCP21
2
2
2
2
2m
CP22P
m2
2
M
m2
2
or
M H2
,
,
,

ADCP22
2
2
2
2
2 m
COTP
Q', Q
ADCOTE

6.2.3 Addressing in the variables intern (example)
6.2.3.1 Variables intern at time less

Part
Significance
Address in VINTM
(local name in routine
COMTHM)
VIMEM

ADVIME


VIHYM
Slq, vp
P, lq
P
ADVIHY

6.2.3.2 Variables intern at time more
Part
Significance
Address in VINTP
(local name in routine
COMTHM)
VIMEP

ADVIME


VIHYP
Slq, vp
P, lq
P
ADVIHY

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6.3 Addressing
R, DRDS, DSDE

6.3.1 Addressing
in
R

Under part of R
Associated
Address in R
R1
v
ADDEME
R2
(v)
ADDEME+NDIM
R3

ADDEP1
1
R4

ADDEP1+1
1
R5

ADDEP2
2
R6

ADDEP2+1
2
R7

ADDETE
R8

ADDETE+1

6.3.2 Addressing
in
DRDS

Part of table DRDS Signification
Address in DRDS
DR1DS


ADDEME, ADCOME
R

R
1
1

+
+


p


DR2DS

ADDEME+NDIM-1, ADCOME
DR1P11
R

ADDEME, ADCP11
1
R1

or
m1+
1+
M
1
1

R

1
R1
R1


m1+
1+
1+

M
1
1
h1
m
DR2P11

ADDEME+NDIM-1, ADCP11
DR1P12
R

ADDEME, ADCP12
1
R1

or
m2+
2+
M
1
1

R

1
R1
R1


m2+
2+
2+
M
1
1
h1


m
DR2P12

ADDEME+NDIM-1, ADCP12
DR1P21
R

ADDEME, ADCP21
1
R1

or
m1+
1 +
M
2
2

R

1
R1
R1


m1+
1 +
1+
M
2
2
H2


m
DR2P21

ADDEME+NDIM-1, ADCP21
DR1P22
R

ADDEME, ADCP22
1
R1

or
m2+
2+
M
2
2

R

1
R1
R1


m2+
2+
2+
M
2
2
H2


m
DR2P22

ADDEME+NDIM-1, ADCP22
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DR1DT
R
R
ADDEME, ADCOTE
1
1


Q'+ +
Q
DR2DT

ADDEME+NDIM-1, ADCOTE
DR3DS

ADDEP1, ADCOME
DR4DS

ADDEP1+1, ADCOME
DR3P11

ADDEP1, ADCP11
DR4P11

ADDEP1+1, ADCP11
DR3P21

ADDEP1, ADCP21
DR4P21

ADDEP1+ 1, ADCP21
DR3DT

ADDEP1, ADCOTE
DR4DT

ADDEP1+ 1, ADCOTE
DR5DS

ADDEP2, ADCOME
DR6DS

ADDEP2+ 1, ADCOME
DR5P11

ADDEP2, ADCP11
DR6P11

ADDEP2+ 1, ADCP11
DR5P21

ADDEP2, ADCP21
DR6P21

ADDEP2+1, ADCP21
DR5DT

ADDEP2, ADCOTE
DR6DT

ADDEP2+ 1, ADCOTE
DR7DS

ADDETE, ADCOME
DR8DS

ADDETE+ 1, ADCOME
DR7P11

ADDETE, ADCP11
DR8P11

ADDETE+ 1, ADCP11
DR7P21

ADDETE, ADCP21
DR8P21

ADDETE+ 1, ADCP21
DR7DT

ADDETE, ADCOTE
DR8DT

ADDETE+1, ADCOTE

6.3.3 Addressing
in
DSDE

Part
Significance
Address in DSDE
(local name with
COMTHM)
DMECDE

ADCOME, ADDEME



p


DMECP1

ADCOME, ADDEP1
p1

p1


p


p

p1 p1
DMECP2

ADCOME, ADDEP2
p2

p2


p


p

p2 p2
DMECDT

ADCOME, ADDETE
T

T


p


p

T
T
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DP11DE
m1
ADCP11, ADDEME

1

1
M1



h1
1 m



DP11P1
m1
1
ADCP11, ADDEP1
1
m1


p

1
p1


1
1
M
M
1
1


p

1
p1


h1
1
1
H
m
1 m

p

1
p1
DP11P2
m1
1
ADCP11, ADDEP2
1
m1


p

2
p2


1
1
M
M
1
1


p

2
p2


h1
1
1
H
m
1 m

p

2
p2
DP11DT
m1
1
ADCP11, ADDETE
1
m1
T T
1
1
M
M
1
1




T
T
h1
1
1
H
m
1 m


T
T
DP12DE
m2
ADCP12, ADDEME

1

2
M1



H2
1 m



DP12P1
m2
2
ADCP12, ADDEP1
1
m1


p

1
p1


2
2
M
M
1
1


p

1
p1


H2
2
1
H
m
1 m

p

1
p1
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DP12P2
m2
2
ADCP12, ADDEP2
1
m1


p

2
p2


2
2
M
M
1
1


p

2
p2


H2
2
1
H
m
1 m

p

2
p2
DP12DT
m2
2
ADCP12, ADDETE
1
m1
T T

2
2
M
M
1
1




T
T

H2
2

1
H
m
1 m


T
T

DP21DE
m1
ADCP21, ADDEME
2

1
M2



h1
2m



DP21P1
m1
1
ADCP21, ADDEP1
2
m2


p

1
p1


1
1
M
M
2
2


p

1
p1


h1
1
2
H
m
2m

p

1
p1
DP21P2
m1
1
ADCP21, ADDEP2
2
m2


p

2
p2


1
1
M
M
2
2


p

2
p2


h1
1
2
H
m
2m

p

2
p2
DP21DT
m1
1
ADCP21, ADDETE
2
m2
T T

1
1
M
M
2
2




T
T

h1
1

2
H
m
2m


T
T

DP22DE
m2
ADCP22, ADDEME
2

2
M2



H2
2 m



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DP22P1
m2
2
ADCP22, ADDEP1
2
m2


p

1
p1


2
2
M
M
2
2


p

1
p1


H2
2
2
H
m
2 m

p

1
p1
DP22P2
m2
2
ADCP22, ADDEP2
2
m2


p

2
p2


2
2
M
M
2
2


p

2
p2


H2
2
2
H
m
2 m

p

2
p2
DP22DT
m2
2
ADCP22, ADDETE
2
m2
T T

2
2
M
M
2
2




T
T

H2
2

2
H
m
2 m


T
T

DTDE
Q'
ADCOTE, ADDEME

Q







DTDP1
Q'
Q'
ADCOTE, ADDEP1
p

1
p1
Q

Q


p

1
p1






DTDP2
Q'
Q'
ADCOTE, ADDEP2
p

2
p2
Q

Q
p

2
p2






DTDT
Q'
Q'
ADCOTE, ADDETE
T T
Q


Q
T
T




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6.4 Algorithm
routine
EQUTHM

YAMEC = MECA (1)
ADDEME = MECA (2)
ADCOME = MECA (3)
NDEFME = MECA (4)
NCONME = MECA (5)

YAP1 = PRESS1 (1)
NBPHA1 = PRESS1 (2)
ADDEP1 = PRESS1 (3)
ADCP11 = PRESS1 (4)
ADCP12 = PRESS1 (5)
NDEFP1 = PRESS1 (6)
NCONP1 = PRESS1 (7)
YAP2 = PRESS2 (1)
NBPHA2 = PRESS2 (2)
ADDEP2 = PRESS2 (3)
ADCP21 = PRESS2 (4)
ADCP22 = PRESS2 (5)
NDEFP2 = PRESS2 (6)
NCONP2 = PRESS2 (7)

YATE = TEMPLE (1)
ADDETE = TEMPLE (2)
ADCOTE = TEMPLE (3)
NDEFT = TEMPLE (4)
NCONT = TEMPLE (5)

CAL COMTHM (

COMPOR OPTION NDIM
NDDL
DIMDEF
DIMCON
NVIMEC
NVIHY, NVITM
NDEFME
NDEFP1
NDEFP2
NDEFT
NCONME
NCONP1
NCONP2
NCONT
YAP1 NBPHA1
YAP2 NBPHA2
DEFGEM (ADDEME) DEFGEM (ADDEP1) DEFGEM (ADDEP2) DEFGEM (ADDETE)
DEFGEP (ADDEME) DEFGEP (ADDEP1) DEFGEP (ADDEP2) DEFGEP (ADDETE)
CONGEM (ADCOME) CONGEM (ADCOTE)

CONGEM (ADCP11) CONGEM (ADCP12) CONGEM (ADCP21) CONGEM (ADCP21)
VINTM (ADVIME) VINTM (ADVIHY) VINTM
(ADVITM)




CONGEP (ADCOME) CONGEP (ADCP11) CONGEP (ADCP21) CONGEP (ADCOTE)
VINTP (ADVIME) VINTP (ADVIHY) VINTP
(ADVITM)
DSDE
DSDE
DSDE
DSDE
(ADCOME, ADDEME) (ADCOME, ADDEP1) (ADCOME, ADDEP2) (ADCOME, ADDETE)
DSDE
DSDE
DSDE
DSDE
(ADCP11, ADDEP1) (ADCP11, ADDEME) (ADCP11, ADDEP2) (ADCP11, ADDETE)
DSDE
DSDE
DSDE
DSDE
(ADCP12, ADDEP1) (ADCP12, ADDEME) (ADCP12, ADDEP2) (ADCP12, ADDETE)
DSDE
DSDE
DSDE
DSDE
(ADCP21, ADDEP2) (ADCP21, ADDEME) (ADCP21, ADDEP1) (ADCP21, ADDETE)
DSDE
DSDE
DSDE
DSDE
(ADCP22, ADDEP2) (ADCP22, ADDEME) (ADCP22, ADDEP1) (ADCP22, ADDETE)
DSDE
DSDE
DSDE
DSDE
(ADCOTE, ADDETE) (ADCOTE, ADDEME) (ADCOTE, ADDEP1) (ADCOTE, ADDEP2)

)
Handbook of Descriptif Informatique
D9.05 booklet: -
HT-66/05/003/A

Code_Aster ®
Version
7.4
Titrate:
New architecture THM. Integration of the equilibrium equations Date
:

22/06/05
Author (S):
C. CHAVANT Key
:
D9.05.03-A Page
: 30/36

If FULL_MECA or RAPH_MECA
If YAMEC
Injection of the terms +
+
+ I in R (ADDEME+NDIM-1)
p
Injection of the terms: -
+
R m
F
in R (ADDEME)
0

If YAP1
+
-
+
+
-
-
Injection of the terms - m1 + m1
1
2
1
2
or
in R (ADDEP1)
1
- m1 - m1 + m1 + m
1
1
Injection of the terms
tM1+
1
+ 1
-
-
or
1
() tM1


T (M1+ + M2+
1
2
+ 1
-
-
+
1
1)
() T (MR. M
1
1)
in R (ADDEP1+1)
IF YAMEC
1+
+
m
1+
2+
+
Injection of the terms: - m F or - (m
F in R (ADDEME)
1
+ m1) m
1
If YATE
Injection of the terms:
T (h1+
1
1+
1
1+
m
1
m

+ 1
-
-
MR. F - 1
MR. F
1
1
1
1

1

m
(
) H m) (m m) T
(
) T1
or

T (H
1+
1
1+
1
2+
2
2+
2
+ 1
-
+
+ 1
-
-
-
1
1
1
1
1

m
(
) H m) (m m) T (H m () h1m) (m m
1
1)
-
t1+ m
1
2 +
2
MR. F - 1
MR. F -
MR. F - 1
-
-
MR. F
1
() T
m
1

T
m
1
() T
m
1
in R (ADDETE)
Injection of the terms
-
1+
1+
HT
1
1
M
1
M or
1
1 - (-)
-
-
HT
m
1 m
1

- T (1+ 1+
H
2
2
1
1
2
2
M
M
1
M
M
1
1 +
+
+
H
m
1 m
1) - (-) T (-
-
h1
1 +
-
-
H
m
1 m
1)
in R (ADDETE+1)
If YAP2
1+
1
1+
2 +
1
2
Injection of the terms + m - m or
in R (ADDEP2)
2
+ m2 + m2 - m2 - m
2
2
Injection of the terms
tM1+
1
+ 1
-
-
or
2
() tM2

T (M1+ +M2+
1 -
2
+ 1
-
-
+
2
2) (
) T (MR. M
2
2)
in R (ADDEP2+1)
IF YAMEC
1+
+
m
1+
2 +
+
Injection of the terms: - m F or - (m
F in R (ADDEME)
2
+ m2) m
2
If YATE
Injection of the terms:

T (h1+
1
1+
1
1+
m
1
m

+ 1
-
-
MR. F - 1
MR. F
2
2
2
2

2

m
(
) H m) (m m) T
(
) T 2
or

T (H
1+
1
1+
1
2+
2
2+
2
+ 1
-
+
+ 1
-
-
-
2
2
2
2
2

m
(
) H m) (m m) T (H m () H2 m) (m m
2
2)
-
t1+ m
1
2 +
2
MR. F - 1
MR. F -
MR. F - 1
-
-
MR. F
2
() T
m
2

T
m
2
() T
m
2
in R (ADDETE)
Handbook of Descriptif Informatique
D9.05 booklet: -
HT-66/05/003/A

Code_Aster ®
Version
7.4
Titrate:
New architecture THM. Integration of the equilibrium equations Date
:

22/06/05
Author (S):
C. CHAVANT Key
:
D9.05.03-A Page
: 31/36

Injection of the terms
- +
+
1
1
T 2
H M
HT
or
m
2
- (1 -) -
-
1
1
2 M
m
2
+
+
+
+

1
1
2
2
-
-
-
-
-
T 2
H M
H
T H
H
m
2
+ 2 M
m
2 - (1 -)
1
1
2
2
2 M
m
2 + 2 M
m
2




in R (ADDETE+1)
If YATE
Injection of the terms: Q'+ Q'-
-
in R (ADDETE)
Injection of the terms -
+
T Q - (1 -)
-

tq in R (ADDETE+1)
Accumulation in vector V:
{}
V = {}
V + [Beautiful T.R
G] {}
Handbook of Descriptif Informatique
D9.05 booklet: -
HT-66/05/003/A

Code_Aster ®
Version
7.4
Titrate:
New architecture THM. Integration of the equilibrium equations Date
:

22/06/05
Author (S):
C. CHAVANT Key
:
D9.05.03-A Page
: 32/36

IF RAPH_MECA or RIGI_MECA_TANG
IF YAMEC
calculation of DR1DS and injection in DRDS (ADDEME, ADCOME)
calculation of DR2DS and injection in DRDS (ADDEME+NDIM-1, ADCOME)
IF YAP1
calculation of DR1P11 and injection in DRDS (ADDEME, ADCP11)
calculation of DR2P11 and injection in DRDS (ADDEME+NDIM-1, ADCP11)
IF NBPHA1 > 1
calculation of DR1P12 and injection in DRDS (ADDEME, ADCP12)
calculation of DR2P12 and injection in DRDS (ADDEME+NDIM-1, ADCP12)
IF YAP2
calculation of DR1P21 and injection in DRDS (ADDEME, ADCP21)
calculation of DR2P21 and injection in DRDS (ADDEME+NDIM-1, ADCP21)
IF NBPHA2 > 1
calculation of DR1P22 and injection in DRDS (ADDEME, ADCP22)
calculation of DR2P22 and injection in DRDS (ADDEME+NDIM-1, ADCP22)
IF YATE
calculation of DR1DT and injection in DRDS (ADDEME, ADCOTE)
calculation of DR2DT and injection in DRDS (ADDEME+NDIM-1, ADCOTE)
IF YAP1
calculation of DR3P11 and injection in DRDS (ADDEP1, ADCP11)
calculation of DR4P11 and injection in DRDS (ADDEP1+1, ADCP11)
IF NBPHA1 > 1
calculation of DR3P12 and injection in DRDS (ADDEP1, ADCP12)
calculation of DR4P12 and injection in DRDS (ADDEP1+1, ADCP12)
IF YAMEC
calculation of DR3DS and injection in DRDS (ADDEP1, ADCOME)
calculation of DR4DS and injection in DRDS (ADDEP1+1, ADCOME)
IF YAP2
calculation of DR3P21 and injection in DRDS (ADDEP1, ADCP21)
calculation of DR4P21 and injection in DRDS (ADDEP1+ 1, ADCP21)
IF NBPHA2 > 1
calculation of DR3P22 and injection in DRDS (ADDEP1, ADCP22)
calculation of DR4P21 and injection in DRDS (ADDEP1+ 1, ADCP22)
IF YATE
calculation of DR3DT and injection in DRDS (ADDEP1, ADCOTE)
calculation of DR4DT and injection in DRDS (ADDEP1+ 1, ADCOTE)
IF YAP2
calculation of DR5P21 and injection in DRDS (ADDEP2, ADCP21)
calculation of DR6P21 and injection in DRDS (ADDEP2+1, ADCP21)
IF NBPHA2 > 1
calculation of DR5P22 and injection in DRDS (ADDEP2, ADCP22)
calculation of DR6P22 and injection in DRDS (ADDEP2+1, ADCP22)
IF YAMEC
calculation of DR5DS and injection in DRDS (ADDEP2, ADCOME)
calculation of DR6DS and injection in DRDS (ADDEP2+ 1, ADCOME)
YAP1 thus:
calculation of DR5P11 and injection in DRDS (ADDEP2, ADCP11)
calculation of DR6P11 and injection in DRDS (ADDEP2+ 1, ADCP11)
IF NBPHA1 > 1
calculation of DR5P12 and injection in DRDS (ADDEP2, ADCP12)
calculation of DR6P12 and injection in DRDS (ADDEP2+ 1, ADCP12)
IF YATE
calculation of DR5DT and injection in DRDS (ADDEP2, ADCOTE)
calculation of DR6DT and injection in DRDS (ADDEP2+ 1, ADCOTE)
IF YATE
calculation of DR7DT and injection in DRDS (ADDETE, ADCOTE)
calculation of DR8DT and injection in DRDS (ADDETE+1, ADCOTE)
IF YAMEC
calculation of DR7DS and injection in DRDS (ADDETE, ADCOME)
calculation of DR8DS and injection in DRDS (ADDETE+ 1, ADCOME)
Handbook of Descriptif Informatique
D9.05 booklet: -
HT-66/05/003/A

Code_Aster ®
Version
7.4
Titrate:
New architecture THM. Integration of the equilibrium equations Date
:

22/06/05
Author (S):
C. CHAVANT Key
:
D9.05.03-A Page
: 33/36

IF YAP1
calculation of DR7P11 and injection in DRDS (ADDETE, ADCP11)
calculation of DR8P11 and injection in DRDS (ADDETE+ 1, ADCP11)
IF NBPHA1 > 1
calculation of DR7P12 and injection in DRDS (ADDETE, ADCP12)
calculation of DR8P12 and injection in DRDS (ADDETE+ 1, ADCP12)
IF YAP2
calculation of DR7P21 and injection in DRDS (ADDETE, ADCP21)
calculation of DR8P21 and injection in DRDS (ADDETE+ 1, ADCP21)
IF NBPHA1 > 1
calculation of DR7P22 and injection in DRDS (ADDETE, ADCP22)
calculation of DR8P22 and injection in DRDS (ADDETE+ 1, ADCP22)

[DRDE] = [DRDS].[DSDE]

DFel

el T
el
.
.
accumulated in MAT
I


(u+, P+, T+
G
N
N
N)
[B] [DRDE] [B
G
]

=
G

6.5
Arguments of the routine of call of the laws of behavior

SUBROUTINE COMTHM (

ARGUMENTS Of INPUT: IN
COMPOR OPTION NDIM
NDDL
DIMDEF
DIMCON
NVIMEC
NVIHY, NVITM
NDEFME
NDEFP1
NDEFP2
NDEFT
NCONME
NCONP1
NCONP2
NCONT
YAP1 NBPHA1
YAP2 NBPHA2
DEMECM
DEP1M
DEP2M
DETM
U, (U)
p, p
p, p
T, T
1
1
2
2
time less
time less
time less
time less
DEMECP
DEP1P
DEP2P
DETP
U, (U)
p, p
p, p
T, T
1
1
2
2
time more
time more
time more
time more
COMECM
COTM


,
Q', Q
p
time less
time less
CP11M
CP12M
CP21M
CP21M
m1
1
, M or
m2
2
, M or
m1
1
, M or
m2
2
, M or
1
1
1
1
2
2
2
2
m1
1
M h1
,
,

m2
2
M H2
,
,

m1
1
M h1
,
,

m2
2
M H2
,
,

1
1
1 m
1
1
1 m
2
2
2m
2
2
2 m
time less
time less
time less
time less
VIMEM
VIHYM
VITMM

internal variables
internal variables
internal variables
méca
hydro
therm
time less
time less
time less
ARGUMENTS OF OUTPUT: OUT
COMECP
COTP


,
Q', Q
p
time more
time more
CP11P
CP12P
CP21P
CP21P
m1
1
, M or
m2
2
, M or
m1
1
, M or
m2
2
, M or
1
1
1
1
2
2
2
2
m1
1
M h1
,
,

m2
2
M H2
,
,

m1
1
M h1
,
,

m2
2
M H2
,
,

1
1
1 m
1
1
1 m
2
2
2m
2
2
2 m
time more
time more
time more
time more
Handbook of Descriptif Informatique
D9.05 booklet: -
HT-66/05/003/A

Code_Aster ®
Version
7.4
Titrate:
New architecture THM. Integration of the equilibrium equations Date
:

22/06/05
Author (S):
C. CHAVANT Key
:
D9.05.03-A Page
: 34/36

VIMEP
VIHYP
VITMP

internal variables
internal variables
internal variables
méca
hydro
therm
time more
time more
time more
DMECDE
DMECP1
DMECP2
DMECDT












p
p
T
T
2
p
1
p


1

2



p
p

p
p


p

p

p


T
T

p

p


2

p
1
p1
2
DP11DE
DP11P1
DP11P2
DP11DT
m1
m1
1
m1
1
m1
1
1
m
1
m
1

1
m

1
1
1








p

p

T
T
2
p
1
p
1
1


2




M
1
1
1
1
1
1
M
M
1

1


M
M
M
M
1


1

1


1


1




T
T

p

p

2
p
1


p
h1
1


2


h1
1
1
H
1 m


h1
1

h1
1

m
1 m
1
H
1
h1
1




m
m
m
m
T
T

p

p


2
p
1
p1
2
DP12DE
DP12P1
DP12P2
DP12DT
m2
m2
2
m2
2
m2
2
1
m
1
m
1

1
m

1
1
1








p

p

T
T

2
p
1
p
2
1


2




M
2
2
2
2
2
2
M
M
1

1


M
M
M
M
1


1

1


1


1




T
T


p

p

2
p
1


p
H2
1


2


H2
2

1
H
1 m


H2
2
H2
2
m
1 m
1
H
1
h1
1




m
m
m
m
T
T


p


p

2
p
1
p1
2
DP21DE
DP21P1
DP21P2
DP21DT
m1
m1
1
m1
1
m1
1
2
m
2
m
2

2
m

2
2
2








p

p

T
T

2
p
1
p
1
1


2




M
1
1
1
1
1
1
M
M
2

2


M
M
M
M
2


2

2


2


2




T
T


p

p

2
p
1


p
h1
1


2


h1
1

2
H
2m


h1
1
h1
1
m
2m
2
H
2
H2
2




m
m
m
m
T
T


p


p

2
p
1
p1
2
Handbook of Descriptif Informatique
D9.05 booklet: -
HT-66/05/003/A

Code_Aster ®
Version
7.4
Titrate:
New architecture THM. Integration of the equilibrium equations Date
:

22/06/05
Author (S):
C. CHAVANT Key
:
D9.05.03-A Page
: 35/36

DP22DE
DP22P1
DP22P2
DP22DT
m2
m2
2
m2
2
m2
2
2
m
2
m
2

2
m

2
2
2








p

p

T
T

2
p
1
p
2
1


2




M
2
2
2
2
2
2
M
M
2

2


M
M
M
M
2


2

2


2


2




T
T


p

p

2
p
1


p
H2
1


2


H2
2

2
H
2 m


H2
2
H2
2
m
2 m
2
H
2
H2
2




m
m
m
m
T
T


p


p

2
p
1
p1
2
DTDE
DTDP1
DTDP2
DTDT
Q'
Q'
Q'
Q'
Q'
Q'
Q'

p

p

T T
2
p
1


p

1
Q


2


Q



Q
Q
Q
Q
Q








p

p

T
T
2
p
1
p


1


2






















)

REAL * 8
DEMECM (NDEFME), DEP1M (NDEFP1), DEP2M (NDEFP2), DETM (NDEFT)
DEMECP (NDEFME), DEP1P (NDEFP1), DEP2P (NDEFP2), DETP (NDEFT)
COMECM (NCONME), CP11M (NCONP1), CP21M (NCONP2), COTM (NCONT)

VIMEM (NVIMEC), VIHYM (NVIHY), VITMM (NVITM)

COMECP (NCONME), CP11P (NCONP1), CP21P (NCONP2), COTP (NCONT)
VIMEP (NVIMEC), VIHYP (NVIHY), VITMP (NVITM)

DMECDE (NCONME, NDEFME), DMECP1 (NCONME, NDEFP1),
DMECP2 (NCONME, NDEFP2), DMECDT (NCONME, NDEFT)
DP11DE (NCONP1, NDEFME), DP11P1 (NCONP1, NDEFP1),
DP11P2 (NCONP1, NDEFP2), DP11DT (NCONP1, NDEFT)
DP21DE (NCONP2, NDEFME), DP21P1 (NCONP2, NDEFP1,
DP21P2 (NCONP2, NDEFP2, DP21DT (NCONP2, NDEFT)

DP12DE (NCONP1, NDEFME), DP12P1 (NCONP1, NDEFP1),
DP12P2 (NCONP1, NDEFP2), DP12DT (NCONP1, NDEFT)
DP22DE (NCONP2, NDEFME), DP22P1 (NCONP2, NDEFP1,
DP22P2 (NCONP2, NDEFP2, DP22DT (NCONP2, NDEFT)

DTDE (NCONT2, NDEFME), DTDP1 (NCONT2, NDEFP1),
DTDP2 (NCONT2, NDEFP2), DTDT (NCONT2, NDEFT)

Handbook of Descriptif Informatique
D9.05 booklet: -
HT-66/05/003/A

Code_Aster ®
Version
7.4
Titrate:
New architecture THM. Integration of the equilibrium equations Date
:

22/06/05
Author (S):
C. CHAVANT Key
:
D9.05.03-A Page
: 36/36

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D9.05 booklet: -
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