A High-order FR-SLAU Scheme for Compressible Inviscid All-speed Flows

This paper presents a high-order all-speed scheme termed FR-SLAU to solve compressible inviscid flows with a wide range of Mach numbers. The method is based on the application of the high-order flux reconstruction method for the space discretization, combined with an all-speed SLAU scheme as the Riemann solver at cell interfaces. Numerical examples demonstrate that pressure errors known for conventional Godunov schemes are avoided. In addition, the new approach is also free from the cut-off reference Mach number that is required by preconditioning techniques. As a result, we obtain a numerical technique allowing the solution of compressible flows with practically all Mach numbers without any modification of the Euler equations. These encourage us to further apply the present method to practical problems involving complex geometries.