Numerical experiments with the split-flux-vector form of the Euler equations

An explicit, finite-volume algorithm based on the flux-vector-splitting concept has been developed for the two-dimensional Euler equations. The method is second-order accurate in space and time, uses body-conforming coordinate systems to map complex geometries to a uniform computational space, and is stable for Courant numbers as high as two. A variable time step, determined by the local Courant number, is used to accelerate convergence of steady-state calculations. This code has been used to calculate lifting and nonlifting transonic flow about airfoils, diffuser flows with shocks, and flows about a cylinder in the supersonic to hypersonic range. Characteristics of this type of split-flux-vector algorithm, as applied to two-dimensional flows with shocks, are discussed.