The accurate solution of the diffusion equation is important for many varied applications. For instance, diffusion equations occur in the modeling of heat conduction, in certain formulations of fluid flow, and in radiation transport. Within the discipline of radiation transport, diffusion equations are used in single-group P1 and Simplified Spherical Harmonics (SPN) calculations, and in Diffusion Synthetic Acceleration (DSA) of transport iterations.
The mesh on which a diffusion problem is to be solved is often dictated by other problem constraints, such as the need to perform a Lagrangian hydrodynamics calculation in conjunction with a diffusion calculation. A mesh type which seems to be gaining prominence in three-dimensional modeling is the unstructured hexahedral mesh. This mesh consists of hexahedra and degenerate hexahedra (prisms, pyramids, tetrahedra, see Figure 1) that are connected in an arbitrary fashion.
This paper develops a numerical method for modeling diffusion on unstructured
hexahedral meshes. The method is an extension of the method described in an
earlier paper by the authors (