On the stability of Godunov-projection methods for incompressible flow (Q1913723)

An analysis of the stability of certain numerical methods for the linear advection-diffusion equation in two dimensions is performed. It is found that various methods currently in use which are based on a Crank-Nicholson type temporal discretization utilizing second-order Godunov methods for explicitly calculating advective terms suffer from a time-step restriction which depends on the coefficients of diffusive terms. A simple modification in the computation of the advective derivatives results in a method with a stability condition that is independent of the magnitude of the coefficients of the diffusive terms.