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

[Matthew Knepley]

On Wed, May 6, 2015 at 2:07 AM, Justin Chang <jychang48 at gmail.com> wrote:

> 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.
>

For some reason, I thought that was taken care of. Please resend. Sorry
about that.

  Thanks,

     Matt


> 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
>>
>
>


-- 
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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