Rotated-hybrid Riemann solver for all-speed flows

Abstract

The contribution deals with numerical solution of compressible flows modeled by the Euler or the Navier–Stokes equations. Addressed flow regimes range from very low Mach number flows to hypersonic flows. The numerical solution is obtained by the finite volume method based on the rotated-hybrid Riemann solver method, where two different Riemann solvers are used in different directions. The combination of the HLL and the HLLC schemes leads to carbuncle-free numerical method. Both the HLL and the HLLC schemes are further modified for improved accuracy and stability in cases with very low Mach number flows. Second order accuracy in space is achieved by the piecewise linear WENO reconstruction while accuracy in time is maintained by the explicit two-stage TVD Runge–Kutta method. The proposed method is validated on many test cases including solution of subsonic flow over an airfoil with M=0.01 or hypersonic flow past circular cylinder with M=20.