一种治愈强激波数值不稳定性的混合方法

Analysis of Numerical Shock Instability and a Hybrid Curing Method

HLLC(Harten-Lax-Leer-contact)格式是一种高分辨率格式,能够准确捕捉激波、接触间断和稀疏波.但是使用HLLC格式计算多维问题时,在强激波附近会出现激波不稳定现象.FORCE(first-order centred)格式在强激波附近表现出很好的稳定性,并且其数值耗散比HLL(HartenLax-Leer)格式小.分析了HLLC格式和FORCE格式在特定流动条件下的稳定性,构造了HLLCFORCE混合格式并且进一步结合开关函数来消除HLLC格式的激波不稳定现象.数值试验表明新构造的混合格式不仅能够消除HLLC格式的激波不稳定现象,还最大程度地保留HLLC格式高分辨率的优点.

HLLC is a high resolution scheme, which can capture shock, contact discontinuity and rarefaction wave accurately. But when it is used to calculate multidimensional problems, the phenomenon of numerical shock instability may appear near the strong shock. Compared with the HLLC scheme, the FORCE scheme is stable near the strong shock, and the related nu- merical dissipation is lower than that of the HLL scheme. The stability of HLLC and FORCE un- der special conditions was analyzed, a hybrid scheme combining the HLLC and FORCE schemes in a special way was constructed, and a switching function to invoke the hybrid scheme in the transverse direction of the shock wave was defined. Numerical experiments demonstrate that the hybrid scheme not only presents good stability near the strong shock, but also retains the high resolution of HLLC.