An S_n Spatial Discretization Scheme for Tetrahedral Meshes

A lumped, linear discontinuous spatial discretization for S_n calculations on tetrahedral meshes is described. This method is designed for applications such as thermal radiative transfer, where resistance to negative solutions and good performance in the thick diffusion limit are essential. The method described has very desirable properties in both the transport regime and the diffusion limit. In particular, the method has enhanced damping of negativities via lumping, second-order accuracy in the transport regime, and a second-order accurate symmetric positive-definite diffusion discretization in the thick diffusion limit that yields well-behaved solutions with unresolved spatial boundary layers. While it is often thought that inaccuracies result when high-aspect-ratio tetrahedra are used to resolve boundary layers, accurate solutions can in fact be computed using high-aspect-ratio tetrahedra if the shape and orientation of the tetrahedra are properly restricted in the boundary layer.