[petsc-users] TS for incompressible NS equations

[Gianluca Meneghello]

Hi,

I would have a question concerning the TS solver in PETSc.

I need to solve the linearized, incompressible Navier Stokes equation
in time. I have reformulated the problem as

B du/dt = J u

where J is the Jacobian of the Navier Stokes equations and u is a
vector containing {u,v,,w,p}.
B is a diagonal matrix which is 0 in the lines corresponding to the
pressure equation (enforcing the divergence free condition) and
Dirichlet BC's and 1 otherwise.

Backward Euler would then solve it as

 u(t+1) = (B-dt J)^-1 B u(t)

as in page 115 of the user guide (is there a typing error there?
Should it be " (B - dt A) u(n+1) = B u(n) " ?)

Using PETSc 3.2, I pass J to the TS object as

TSSetRHSFunction(ts,PETSC_NULL,TSComputeRHSFunctionLinear,PETSC_NULL);CHKERRQ(ierr);
TSSetRHSJacobian(ts,A,A,TSComputeRHSJacobianConstant,PETSC_NULL);CHKERRQ(ierr);

but I don't understand how I can set B (or whether I am using a wrong approach).

Thanks in advance for your help

Gianluca

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