Comparison of finite volume flux vector splittings for the Euler equations

Abstract

A flux-splitting method in generalized coordinates has been developed and applied to quasi-one-dim ensional transonic flow in a nozzle and two-dimensional subsonic, transonic, and supersonic flow over airfoils. Computational results using the Steger-Warming and Van Leer flux splittings are compared. Discussed are several advantages of a MUSCL-type approach (differencing followed by flux splitting) over a standard flux differencing approach (flux splitting followed by differencing) . With an approximately factored implicit scheme, spectral radii of 0.978-0.930 for a series of airfoil computations are obtained, generally decreasing as a larger portion of the flow becomes supersonic. The Van Leer splitting leads to higher convergence rates and a sharper representation of shocks, with at most two (but more often, one) zones in the shock transition. The second-order accurate one-sided-difference model is extended to a third-order upwind-biased model with a small additional computational effort. The results for both the second- and third-order schemes agree closely in overall features to a widely used central difference scheme, although the shocks are resolved more accurately with the flux splitting approach.