Improvement of the genuinely multidimensional ME-AUSMPW scheme for subsonic flows

Since proposed, the genuinely multidimensional Riemann solvers have been attracting more attentions because it considers the waves normal and parallel to the cell interfaces at the same time. However, all these methods are built upon the hyperbolic property of the compressible Euler equations. Therefore, they can not be applied to solve the Euler equations in steady subsonic cases which are with the elliptic property. In this study, a novel multidimensional Riemann solver called MULE-AUSMPWM (Multidimensional E-AUSMPW Modified) is proposed. It is built upon the Zha–Bilgen splitting procedure and adopts the Balsara's multidimensional wave model as the ME-AUSMPW scheme. In addition, it improves the ME-AUSMPW scheme's accuracy at subsonic speeds by avoiding simulating the convective fluxes in fully upwind manners. Extensive numerical tests, such as the two dimensional Euler problem, the one dimensional moving contact discontinuity case, the two-dimensional double Mach reflection case, the two-dimensional Riemann problem, and the turbulent flow past a 2d NACA0012 airfoil case, are conducted. Results illustrate that the MULE-AUSMPWM scheme proposed is capable of simulating compressible complex flows and improving the existing multidimensional Riemann solvers' accuracy at subsonic speeds remarkably.