i am working on high resolution upwind methods (godunov schemes) with an unsplit finite volume approach for multidimensional problems. the courant number for 1d schemes is given by c=a dt/dx (a: wave speed). what kind of stability condition must i consider for the unsplit multidimensional case.

thanks manfred

Collela, P. 1990. Multidimensional Upwind Methods for Hyperbolic Conservation Laws. JCP. 87.pp171-190

I think this is what you are looking for...Or at least a start...

JCP=Journal of Computational Physics

As far as I know, and what I have done is this: For each flux calculation direction, (normal to each cell surface) I calculated (approximated) maximum wave speed. I used the maximum of these speeds to calculate minimum time step (to be used in my explicit method) from the Courant formula you have written.

If there are limitations of this method especially in transient calculations, I would be happy to know. Thanks every one.