A FLUX-LIMITED MODEL OF PARTICLE DIFFUSION AND VISCOSITY

The standard diffusion equation that is used to model diffusive phenomena suffers from a serious defect, namely it violates causality. Levermore and Pomraning developed a flux-limited diffusion theory (FDT) for radiative transfer that overcomes this limitation. The present paper develops extensions of FDT which can be used to model steady state particle diffusion and viscous transport. The key improvement is that the diffusing particles are allowed to have a range of speeds, whereas in FDT they are assumed to have a single speed (which is appropriate for radiation). Expressions are given for the diffusion constant and the viscosity coefficient in steady state flows with bulk motion. Heuristic prescriptions are also presented for possible application in time-dependent moving flows.