DiffusionPhysicsBase

This is a base class for the derived Physics actions setting up objects to solve the diffusion equation with a particular discretization.

The diffusion equation solved is:

utDu(x)f(x)=0\dfrac{\partial u}{\partial t} - \nabla \cdot D \nabla u(\vec{x}) - f(\vec{x}) = 0

with Dirichlet boundary conditions:

u(x)=gu(\vec{x}) = g

and / or Neumann boundary conditions:

Dun=hD\dfrac{\partial u}{\partial n} = h

over the boundaries specified by the "dirichlet_boundaries" and "neumann_boundaries" parameters respectively.

The values set at the Dirichlet boundary conditions, gg, and Neumann boundary conditions, hh, are set by the "boundary_values" and "boundary_fluxes" respectively.