[petsc-users] Computing time derivatives in the residual for TS

[Mani Chandra]

Hi,

Suppose the following is the residual function that TS needs:

void residualFunction(TS ts, PetscScalar t, Vec X, Vec dX_dt, Vec F, void
*ptr)

and this returns the following finite volume residual at each grid point

dU_dt + gradF + sourceTerms = 0

where dU_dt are the time derivatives of the conserved variables.

The value of dU_dt needs to be computed from the values of the time
derivatives of the primitive variables given in dX_dt, i.e. dU_dt is an
analytic function of dX_dt. But is it possible to compute dU_dt numerically
using the vector X and it's value at a previous time step like the
following?

dU_dt = (U(X) - U(X_old) )/dt -- (1)

(instead of analytically computing dU_dt which is a function of the vectors
X and dX_dt which is hard to do if the function is very complicated)

So, is computing dU_dt using (1) permissible using TS? The jacobian will be
correctly assembled for implicit methods?

Cheers,
Mani
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