64 / 2019-09-27 16:58:59

A novel multidimensional Riemann solver for Euler Equations

Multidimensional;,Riemann Solver,Euler Equations,Flux Splitting

A novel multidimensional Riemann solver for Euler equations called MULE-AUSMPWM (Multidimensional E-AUSMPW Modification) is proposed. By adopting the Balsara’s multidimensional wave model, this solver considers both the waves orthogonal to the cell interfaces and the waves transverse to the cell interfaces. Based on the Zha-Bilgen splitting procedure, it avoids the complex formulation of Balsara’s multidimensional HLLC method to be with a high resolution in capturing contact discontinuities. Also, it improves the accuracy at subsonic speeds by avoiding simulating the convective fluxes in fully upwind manners as the MULTV and the ME-AUSMPW scheme. Systematic numerical cases, including 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 carried out. Results show that the MULE-AUSMPWM scheme proposed in this manuscript is with a high resolution in simulating compressible complex flows and improves the existing multidimensional flux splitting methods’ accuracy at subsonic speeds remarkably. Therefore, it is promising to be widely used in both scholar and engineering areas.