[firedrake] Enforcing slip boundary condition strongly

[Lawrence Mitchell]

Hi Justin,

> On 9 Jul 2015, at 21:28, Justin Chang <jychang48 at gmail.com> wrote:
> 
> Hi everyone,
> 
> I am solving a mixed poisson (aka: Darcy) problem using the VMS formalism (Masud and Hughes, CMAME, 2002) which enables one to use equal order lagrangian interpolation. In this formulation, the flux/velocity is prescribed strongly and the pressure is prescribed weakly, like how it's done with RT0 elements.
> 
> The main difference is that velocity is now a VectorFunctionSpace as opposed to a FunctionSpace. My question is, how would I implement the flux boundary condition in a Dirichlet sense? Say I am working with a unit square for now. I want to enforce v_x = some value(s) for x=0/x=1, and v_y - some values(s) for y = 0/y = 1. How would this be done in Firedrake?


I /believe/ the combination of the two branches in PyOP2 and Firedrake described below will do what you want.

PyOP2, branch bc-components (pull request https://github.com/OP2/PyOP2/pull/450)

Firedrake, branch bc-components (pull request https://github.com/firedrakeproject/firedrake/pull/551)

With these, you can do:

V = VectorFunctionSpace(mesh, "CG", 1)
P = VectorFunctionSpace(mesh, "CG", 1)

W = V*P

# boundary condition for x-component of velocity space.
bcvx = DirichletBC(W.sub(0).sub(0), scalar_value, boundary_ids)
# and for y-component
bcvy = DirichletBC(W.sub(0).sub(1), scalar_value, boundary_ids)

solve(..., bcs=[bcvx, bcvy])

You can either try using those branches directly or else wait until they're merged and update to a newer master.  But if you try them and find problems, please do update the pull requests with comments.

Cheers,

Lawrence
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