Conservative finite differences as an alternative to finite volume for compressible flows

Abstract

Finite Volume schemes are the natural choice when simulating flows with shocks, since conservation is essential in the physics and as such in the simulation of this phenomenon. But finite difference schemes can be conservative as well. Conservation requires in such schemes a high internal consistency of the spatial and the temporal discretization. We present a skew-symmetric finite difference scheme, which is fully conservative due to its consistency, still easy to implement and numerically efficient. A variety of different flow configurations containing shocks and turbulence are presented.