Jane,
can you write down the discretized weak formulation you using?
Is there any paper showing well-posedness and suitable error estimates for
that discretization?
Best,
Daniel
Am Mittwoch, 6. Februar 2019 17:22:28 UTC+1 schrieb jane...@jandj-ltd.com:
>
> Hi all,
>
> I am trying to solve a system of equations that do this:
> Stokes to solve for v_r and p_r for one fluid (viscous rock), I use these
> solutions on the RHS of a Darcy type equation solved like step-20 for the
> pressure p_f in the fluid in the domain. Using the 3 solutions, I update
> another component (porosity - using a simple time dependent equation like
> dphi/dt = rhs(pr-pf)) and put it back in the Stokes equation and so on....
>
> One of my conditions for the Darcy eqn is that for the top boundary, the
> pressure there equals pr found previously.
>
> Looking at the output, my values for p_f at the top boundary does not
> equal the p_r just found. This is causing a massive issue as my porosity
> equation needs pr-pf to be 0 (or at least very small) at the top boundary,
> and this seems to be causing a real mess. I'm guessing because it's weakly
> imposed, there might be issues.
>
> Does anyone have any suggestions on what to do for this?
>
> My base profile for the equations separately all work and have been
> verified with MMS. With test values of the porosity, I have also verified
> that the profiles separately give me what I expect (which then gives me
> pr-pf monotonic at least, but with what is happening at the top, this bit
> is messed up).
>
>
> For the boundary condition, I am doing:
>
> for (unsigned int face_no=0;
>
> face_no<GeometryInfo<dim>::faces_per_cell;
>
> ++face_no)
>
> if (cell->face(face_no)->at_boundary()
>
> &&
>
> (cell->face(face_no)->boundary_id() == 1)) // top has boundary id 1
>
> {
>
> fe_face_values_pf.reinit (cell, face_no);
>
> fe_face_values_rock.reinit (vr_cell, face_no);
>
>
> fe_face_values_rock[pressure].get_function_values (solution_rock,
> pr_boundary_values);
>
>
> // DIRICHLET CONDITION FOR TOP. pf = pr at top boundary
>
> for (unsigned int q=0; q<n_face_q_points; ++q)
>
> {
>
> for (unsigned int i=0; i<dofs_per_cell; ++i)
>
> {
>
> local_rhs(i) += -( fe_face_values_pf[velocities].value (i, q) *
>
> fe_face_values_pf.normal_vector(q) *
>
> pr_boundary_values[q] *
>
> fe_face_values_pf.JxW(q));
>
> }
>
> }
>
> }
>
>
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