一种健壮的TV通量分裂格式

随着计算流体力学的快速发展，设计精确、高效并且健壮的数值格式变得尤为重要。Toro等^8]提出的TV通量分裂格式表现出简单、高效和精确分辨接触间断等优点，但是在计算一些多维算例时会出现数值激波不稳定现象。两波近似的HLL格式在计算中非常高效和健壮，但是不能分辨接触间断大大地限制了其应用。本文对TV通量分裂格式进行稳定性分析，据此提出一种混合格式来消除TV格式的数值激波不稳定性。数值试验表明，本文构造的混合格式不仅保留了原始TV格式的优点，而且具有更好的健壮性，在计算二维问题时不会出现数值激波不稳定现象。

A robust TV flux splitting scheme

With the rapid development of computational fluid dynamics,it is particularly important to design accurate,efficient and robust numerical schemes.Recently the TV flux splitting scheme proposed by Toro and Vázquez shows advantages of simplicity,efficiency and resolving contact discontinuities accurately,but numerical shock instability will occur when calculating some multidimensional examples.The two-wave approximate HLL scheme is very efficient and robust in calculations,but failure to capture contact discontinuities limits its application.In this paper,the stability analysis of TV flux splitting scheme is carried out,and a hybrid scheme is proposed to eliminate numerical shock instability of TV scheme.Numerical experiments show that the hybrid scheme presented here not only preserves the advantages of the original TV scheme but also has better robustness,eliminating numerical shock instability when calculating two-dimensional problems.