[petsc-users] Matrix-free TS

[Matthew Knepley]

On Mon, Mar 27, 2017 at 12:14 PM, Amneet Bhalla <mail2amneet at gmail.com>
wrote:

>
> Hi Folks,
>
> I am thinking of trying TS module of PETSc to free myself of maintaining
> time stepping part of the code and to try different
> time integrators easily. The problem that I am considering is
> incompressible
> Navier Stokes with variable coefficients solved using  projection method.
> The method would involve solving equations in two parts:
>
> rho u*_t - div ( sigma) = RHS( u_explicit)  ---- (1)
>
> and then projecting u* onto divergence free u by solving a pressure
> Poisson equation  (Eq 2).
>
>  Here sigma = mu ( u_ij + u_ji) is the viscous stress
> tensor.
>
> I have custom solvers for solving (1) and (2) using geometric MG  wrapped
> as
> a PCSHELL to MATSHELL obtained by discretizing (1) and (2) say by
> Backward Euler.
>
> Is it possible to wrap Eq (1) and (2) in TS in matrix-free form and then
> solve for
> velocity and pressure using projection method using matrix-free solvers?
>

I see at least two ways to do this:

1) Timestep your momentum equation, and put the projection step in
TSPoststep()

2) Formulate the combined system implicitly as a DAE and then use a
block-Jacobi
    solver for it.

1) sounds easier and matches your current code.

   Matt


> Thanks,
> --
> --Amneet
>
>
>
>


-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener
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