Fully-discrete numerical transfer in diffusive regimes

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Abstract
We study the behavior of two fully-discrete numerical schemes (the step scheme and the cell-edge even-parity scheme) for the transfer equation in diffusive regimes with coarse meshes. The diffusion boundary conditions for these numerical schemes are derived through a boundary layer analysis that matches the interior discrete diffusion approximation to the boundary data for the discrete transfer equation. Requiring that the resulting discrete diffusion boundary condition to be a good approximation to the diffusion boundary conditions obtained for the transfer equation then gives constraints on the discretization. It is shown that the quadrature set Bn developed in our earlier paper [9] gives accurate extrapolated endpoints, while new discrete one-way flux boundary conditions introduced here that are based on the discrete W-function, give accurate forcing terms. Consequently, as we then demonstrate numerically, these new schemes give more accurate results than traditional schemes for problems containing diffusive regimes that involve boundaries and interfaces.

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