激波数值稳定的低耗散修正HLLEM格式与应用

A low-dissipation modified HLLEM scheme with numerical stability for shock waves and its application

在航空航天领域,含强激波的可压缩流动问题的数值模拟具有重要的科学工程意义。许多流行的数值通量格式(如CFD工业软件中普遍使用的Roe格式)在计算强激波时会出现不同形式的数值不稳定现象,这些非物理现象极大影响了模拟结果的可靠性。本文采用平衡对流耗散与声耗散的方法来增强格式的激波数值稳定性,通过简单修改波速的计算将其应用到HLLEM通量格式上。不同于传统上通过增加数值耗散的方法来消除格式的激波数值不稳定性,本文采用的策略不仅简单而且还能局部减少格式对非线性波的数值耗散。此外,采用THINC重构结合BVD算法来进一步减少数值耗散项中网格界面两侧的密度差,从而提高格式对于线性波的分辨率。稳定性分析证明了平衡对流耗散与声耗散可以有效地消除激波数值失稳现象。一系列经典的数值实验验证了构造的激波捕捉格式的高分辨率和强稳定性。

In the field of aerospace engineering,the numerical simulation of compressible flows with strong shock waves has important scientific and engineering significance.Many popular flux schemes,such as the Roe scheme commonly used in industrial CFD software,will encounter different forms of instability while calculating strong shock waves.These nonphysical phenomena severely affect the reliability of simulation results.The method of balancing advective dissipation and acoustic dissipation is used to enhance the shock stability of the scheme,and it can be applied to the HLLEM scheme by simply modifying the calculation of wave speeds.Unlike traditional methods that increase numerical dissipation to eliminate the shock instability,the strategy adopted here is not only simple but also locally reduces the numerical dissipation for nonlinear waves.In addition,the THINC reconstruction and BVD algorithm are used to further reduce the density difference between two sides of the interface in the numerical dissipation term,so as to improve the resolution for linear waves.The stability analysis shows that the strategy of balancing the advective dissipation and the acoustic dissipation can effectively eliminate the numerical shock instability.A series of classical numerical experiments demonstrate the high resolution and strong stability of the shock-capturing scheme constructed here.