Diffusion Theory via Asymptotics
G. C. Pomraning · Operator theory · 1991
It is known that classic diffusion theory can lead to negative scalar fluxes if the external source of particles is anisotropic. The usual derivation of diffusion theory, via a truncated spherical harmonics expansion, gives no consistent way of dealing with this lack of positivity. In this paper we show that asymptotic methods can be used to derive a positive diffusion equation. These same ideas can be used to produce alternate diffusion theories which should be more accurate than classic diffusion theory for diffusive problems. A specific such modified diffusion theory is developed in some detail. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.