A technique for high-order treatment of diffusion terms in semi-lagrangian schemes

Abstract

We consider in this paper a high-order, semi-Lagrangian technique to treat possibly degenerate advection-diffusion equations, which has been proposed in similar forms by various authors. The scheme is based on a stochastic representation formula for the solution, which allows to avoid the splitting between advective and diffusive part of the evolution operator. A general theoretical analysis is carried out in the paper, with a special emphasis on the possibility of using large Courant numbers, and numerical tests in one and two space dimensions are presented. © 2010 Global-Science Press.