CFL Condition

Matt Umbel

This question deals with the Courant number and the CFL condition (C<1) that devines the stability of many numerical methods. My question is this, is it true that the strict CFL condition is only for explicit methods for solving highly hyperbolic PDEs, where the numerical domain of influence is in one direction? That direction being forward in time.

I have heard at least one experienced CFD person claim that it is always necessary to have C<1 or C~1 or else the CFL condition is violated, even when dealing with an implict scheme. However, since the numerical domain of influence with an implicit or partially implicit method is not entirely forward, isn't it meaningless to discuss requirement of the CFL condition for an implicit case?

I realize as C gets very large transient accuracy may become an issue. However, is there some other stipulations, other than stability for explicit solutions of hyperbolic PDEs, that are implied when someone discusses the CFL condition?

Thanks