[petsc-users] Applying Natural Boundary Conditions using PETSc FEM Technology

[Matthew Knepley]

On Tue, Dec 12, 2023 at 12:23 PM Brandon Denton via petsc-users <
petsc-users at mcs.anl.gov> wrote:

> Good Afternoon,
>
> I am currently working on an Inviscid Navier-Stokes problem and would like
> to apply DM_BC_NATURAL boundary conditions to my domain. Looking through
> the example files on petsc.org, I noticed that in almost all cases there
> are the following series of calls.
>
> PetscCall(DMAddBoundary(dm, DM_BC_NATURAL, "wall", label, 1, &id, 0, 0,
> NULL, NULL, NULL, user, &bd));
> PetscCall(PetscDSGetBoundary(ds, bd, &wf, NULL, NULL, NULL, NULL, NULL,
> NULL, NULL, NULL, NULL, NULL, NULL));
> PetscCall(PetscWeakFormSetIndexBdResidual(wf, label, id, 0, 0, 0, f0_bd_u,
> 0, NULL));
>
> Is this the standard way of applying Natural boundary conditions in PETSc
> for FEM?
>

Yes. The problem is that AddBoundary was designed just to deliver boundary
values, but inhomogeneous Neumann conditions really want weak forms, and
the weak form interface came later. It is a little clunky.


> Also, I noticed in the signature for the  f0_bd_u function, there is a
> const PetscReal n[] array. What is this array and what information does it
> hold. Is it the normal vector at the point?
>

That is the normal at the evaluation point.

  Thanks,

     Matt


> static void f0_bd_u(PetscInt dim, PetscInt Nf, PetscInt NfAux, const
> PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const
> PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const
> PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const
> PetscScalar a_x[], PetscReal t, const PetscReal x[], const PetscReal n[],
> PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
>
> Thank you in advance for your time.
> Brandon
>
>
>
>
>

-- 
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

https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
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