A Robust Smoother for Convection-Diffusion Problems with Closed Characteristics

Abstract

In this paper we analyze a model problem for the convection-diffusion equation where the reduced problem has closed characteristics. A full upwinding finite difference scheme is used to discretize the problem. Additionally to the strength of the convection, an arbitrary amount of crosswind-diffusion can be added on the discrete level. We present a smoother which is robust w.r.t. the strength of convection and the amount of crosswind-diffusion. It is of Gauss–Seidel type using a downwind ordering. To handle the cyclic dependencies a frequency-filtering algorithm is used. The algorithm is of nearly optimal complexity ?(n log n). It is proved that it fulfills a robust smoothing property.