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.

自从提出以来，真正的多维黎曼求解器已经引起了更多的关注，因为它同时考虑了垂直且平行于单元界面的波。但是，所有这些方法都是基于可压缩的Euler方程的双曲性质。因此，它们不能用于求解具有椭圆性质的稳定亚音速情况下的欧拉方程。在这项研究中，提出了一种新颖的多维黎曼求解器，称为MULE-AUSMPWM（Multiple E-AUSMPW Modified）。它建立在Zha-Bilgen分裂程序的基础上，并采用Balsara的多维波模型作为ME-AUSMPW方案。此外，它避免了以完全迎风的方式模拟对流通量，从而提高了ME-AUSMPW方案在亚音速下的精度。广泛的数值测试 如二维Euler问题，一维运动接触不连续情况，二维Double Mach反射情况，二维Riemann问题以及经过2d NACA0012翼型情况的湍流。结果表明，所提出的MULE-AUSMPWM方案能够模拟可压缩的复杂流，并能够在亚音速下显着提高现有的多维Riemann求解器的精度。