Characteristics methods in thick diffusive problems

The authors analyze and test the performance of characteristics methods (CMs) on problems that contain diffusive regions. Their asymptotic analysis predicts that as spatial cells become optically thick and highly scattering, these methods behave exactly like discontinuous finite-element methods (DFEMs). The authors test this prediction computationally for the linear and bilinear characteristics methods on rectangular grids in XY geometry. Their analysis further predicts that certain simplified CMs (and hence the analogous DFEMs) will perform extremely well on triangular grids in XY geometry and on tetrahedral grids in XYZ geometry