[petsc-users] advection-diffusion pointwise function for FEM

[Justin Chang]

Matt,

Yes I would actually use a[] in this case. Back then, I think I was trying
to take the derivative of the auxiliary which i had declared to be
piece-wise constant.

The auxiliary a[] is the gradient of pressure (times permeability over
viscosity) obtained from solving the Darcy equation as a Laplacian. This
part is solved separately, projected as cell-wise velocity, and inputted as
an auxiliary for the advection-diffusion problem.

Speaking of which, have you had a chance to look into
DMPlexProjectFieldLocal(...) not projecting dirichlet BC constraints? I
realize that the "small example" I gave you wasn't small at all, so I can
send you a smaller and simpler one if needed.

Thanks,
Justin

On Tue, May 5, 2015 at 3:34 PM, Matthew Knepley <knepley at gmail.com> wrote:

> On Sat, Apr 4, 2015 at 11:54 AM, Justin Chang <jchang27 at uh.edu> wrote:
>
>> Hi everyone,
>>
>> I want to include advection into my diffusion FEM code (I am assuming a
>> small Peclet number so stability isn't an issue ATM). That is I want to
>> incorporate the second term as a pointwise function:
>>
>> du/dt + v * grad[c] - div[grad[c]] = f
>>
>> Where v is the velocity (obtained from the auxiliary term a_x[]). For the
>> residual, would it be of the following form:
>>
>
> 1) I would think you would use a[] instead. What is your velocity the
> gradient of?
>
>
>> f0_u(const PetscScalar u[], const PetscScalar u_t[], const PetscScalar
>> u_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar
>> a_x[], const PetscReal x[], PetscScalar f0[]) {
>>
>>   PetscInt d;
>>   f[0] = u_t[0];
>>   for (d = 0; d < spatialDim; ++d) f0[0] += a_x[d]*u_x[d];
>>
>> }
>>
>> What about the jacobian? My guess would be to use g1(...) but what would
>> the inside of this function be?
>>
>
> Yes it would be g1. The indices for the output are f,g,dg. I am guessing
> that c is a scalar, so f = {0}, g = {0}, dg = {0, 1}
> for 2D, so g1 would have two terms,
>
>   g1[0] = a[0];
>   g1[1] = a[1];
>
>   Thanks,
>
>     Matt
>
>
>> Thanks,
>>
>>
>> --
>> Justin Chang
>> PhD Candidate, Civil Engineering - Computational Sciences
>> University of Houston, Department of Civil and Environmental Engineering
>> Houston, TX 77004
>> (512) 963-3262
>>
>
>
>
> --
> 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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