Numerical simulations of degenerate transport problems

17th AIAA Computational Fluid Dynamics Conference, 2005

Applied Numerical Mathematics, 1990

Numerical treatment of certain diffusion problems via indirect (analytical) methods requires solving boundary-value problems for degenerate parabolic equations or systems. Degeneracy may arise from coordinate singularity (polar coordinates) or other more intrinsic reasons. Examples of degenerate diffusions can be found in wave propagation in random media, genetics and mathematical theory of evolution. Methods based on suitable finite difference schemes either suggested by the structure of the problems (symmetry, formally obtained limiting-equations, etc.) or by the conservation of certain quantities, as it happens for their continuous analogue, are introduced to compute the solutions with accuracy and stability.