# [petsc-users] Solving a coupled multi-physics problem.

Rahul Samala srahul_05 at yahoo.co.in
Tue Jul 2 06:30:19 CDT 2019

```Hello PetSc users,

I request suggestions on how to do a coupled problem, in my case coupling between multiphase flow in porous media and deformation of porous media.I have successfully written and validated the flow code with 3 degrees of freedom (S-saturation, P-pressure, T-Temperature)
which uses SNES solver inside a time loop.  I have to use KSP solve for the deformation problem which has 1 degree of freedom (u-displacement).
For the coupled problem, the flow part now requires the displacement vector and the deformation part requires
the pressure field.

I have written a pseudo-code below.
My idea is to use the second solution vector (displacement) in FormFunctionLocal belonging to SNES.
Since the DM used by SNES can be used for only one problem, a clone is made to be used for KSP.
Is this approach the correct way to solve this coupled problem.

typedef struct {
PetscScalar s; // Saturation
PetscScalar p; // Pressure
PetscScalar T; // Temperature
} Field;

typedef struct {
PetscScalar u; // Displacement
} Field2;

FormFunctionLocal(DMDALocalInfo *info, Field *sol, Field2 *sol2, Field *f, AppCtx *user)
{
........................
}

main()
{
DM   da, newda;
Vec  sol;
Vec  sol2;
SNES  snes;
KSP   ksp;

SNESCreate(......, &snes);
DMDACreate1d(........,&da);
.
.
SNESSetDM(snes, da);
DMClone(da, &newda);
KSPCreate(.........,&ksp);
KSPSetDM(ksp, newda);
.
.
DMDASetUniformCoordinates(da,...........);
DMDASNESSetFunctionLocal(da,...........,FormFunctionLocal);
.
DMCreateGlobalVector(da, &sol);
DMCreateGlobalVector(newda, &sol2);    // This sol2 of type Field2 is passed to FormFunctionLocal.
.
do { // Time loop

SNESSolve(snes,....);
.
.
KSPSolve(ksp,......);
.
.
}while(criteria);
}

Thank you,Rahul.

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