Second-order upwinding through a characteristic time-step matrix for compressible flow calculations

An efficient multidimensional scheme is constructed for solving the compressible Euler equations. It is deduced from a centered scheme of the Lax-Wendroff type by using a special time-step in the numerical flux, namely a matricial characteristic time-step. This produces a compact second-order upwinding in a very simple way and leads to accurate non-oscillatory solutions without limiters, entropy correction, or other dissipative correction. The design principle is analysed for hyperbolic systems of conservation laws. It is shown to be close to and less dissipative than a genuinely multidimensional upwinding. Numerical applications are presented for subsonic, transonic, and supersonic aerodynamic problems. (C) 1998 Academic Press.