On Destabilizing Implicit Factors in Discrete Advection-Diffusion Equations

Abstract

In the present paper, we find necessary and sufficient stability conditions for a simple one-time step finite difference discretization of an N -dimensional advection diffusion equation. Furthermore, it is shown that when the implicit factors differ in each direction, a strange behavior occurs: By increasing one implicit factor in only one direction, a stable scheme can become unstable. It is thus suggested to use a single implicit direction (for efficient computing), or the same implicit factor in each direction.