A fifth order alternative Compact-WENO finite difference scheme for compressible Euler equations

Abstract

In this paper, we propose an alternative formulation of conservative fifth order finite difference compact Weighted Essentially Non-Oscillatory (WENO) schemes to solve compressible Euler equations. Comparing with the classical conservative finite difference Compact-WENO scheme, its reconstruction procedure is applied to the point values rather than the traditional flux functions, then the HLLC (Harten, Lax and van Leer) and the local Lax-Friedrichs flux functions can be used to compute the interface fluxes in this framework. To maintain positivity of density and pressure, the parametrized positivity satisfying flux limiter is coupled with the proposed scheme for problems with extreme conditions. A number of testing cases including Titarev-Toro problem, the planar Sedov blast-wave problem, Riemann problems, double Mach reflection problem, shock diffraction problem and Kelvin-Helmholtz instability problem are presented to demonstrate the high resolution of the proposed compact scheme.