A Smooth Transition Model between Kinetic and Diffusion Equations

Abstract

This paper presents a model which provides a smooth transition between a kinetic and a diffusion domain. The idea is to use a buffer zone, in which both diffusion and kinetic equations will be solved. The solution of the original kinetic equation will be recovered as the sum of the solutions of these two equations. We use an artificial connecting function which makes the equation on each domain degenerate at the end of the buffer zone. Thus no boundary condition is needed at the transition point. This model avoids the delicate issue of finding the interface condition or iteration in a typical domain decomposition method that couples a kinetic equation with hydrodynamic equations. A new asymptotic-preserving method for this model is introduced, and numerical examples are used to validate this new model and the new numerical method.