On destabilizing implicit factors in discrete advection-diffusion equations (Q1326678)

Necessary and sufficient conditions for the stability of a simple one- time step finite difference discretization of an \(N\)-dimensional advection-diffusion equation are derived. Furthermore it is shown that when the implicit factors differ in each direction, the following abnormal behavior occurs: By increasing one implicit factor in only one direction a stable schema can become unstable. For this situation it is suggested to use a single implicit direction for efficient computing or the same implicit factor in each direction.