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| 全速域可压缩流动的低耗散强鲁棒数值格式 |
| A low-dissipation robust numerical scheme for all-speed compressible flows |
| 投稿时间：2025-06-25 修订日期：2025-07-18 |
| DOI： |
| 中文关键词: 三维欧拉方程组 HLLEM格式 压力耗散项 激波数值不稳定现象 低马赫数流 |
| 英文关键词:Three-dimensional Euler equations HLLEM scheme Pressure-dissipation term Numerical shock instability phenomenon Low-Mach number flows |
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| 中文摘要: |
| HLLEM格式具有保正性、满足熵条件且能准确捕捉各类波系，是计算对流数值通量一种流行的数值方法。然而，格式固有的两个缺陷限制了它的应用：一是在捕捉激波时出现的各类数值不稳定现象；二是在计算低速流动问题时会出现计算精度下降等问题。为消除激波计算中的各类不稳定现象，在原始的HLLEM通量中添加压力耗散项。此外，利用界面马赫数定义控制函数来调控动量方程中由速度差造成的过多耗散来改进格式模拟低速流动的性能。一系列基准测试验证了改进格式在模拟高速和低速流动问题中的精度和鲁棒性。 |
| 英文摘要: |
| The HLLEM scheme is positive-preserving, satisfies the entropy condition and can accurately capture various waves. It is a popular numerical method for calculating convective numerical fluxes. However, two inherent flaws of the scheme limit its application: one is the various numerical instability phenomena that occur when capturing shock waves; Secondly, it suffers from a loss of computational accuracy when solving low-speed flow problems, among other issues. To eliminate various unstable phenomena in calculations of shock waves, a pressure-dissipation term is added to the original HLLEM flux. In addition, the interface Mach number is utilized to define the control function to regulate the excessive dissipation caused by the velocity difference in the momentum equations, thereby improving the performance of the scheme in simulations of low-speed flows. A series of benchmark test cases verify the accuracy and robustness of the proposed scheme in simulating high- and low-speed flow problems. |
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