Low-dissipation shock-capturing methods usually suffer from various forms of shock instabilities, such as the notorious carbuncle phenomenon, in simulations of hypersonic flows. Many strategies for tackling the shock instability of flux difference splitting schemes, such as HLLC and Roe schemes, have been proposed while little work has been undertaken on the shock instability of flux splitting schemes. In this paper, we are concerned with the shock instability of a convection-pressure flux splitting scheme. By means of a linearized perturbation analysis, it shows that all of the perturbations in the streamwise direction are damped, while the perturbations of density and shear velocity in the transverse direction are undamped. Due to the special symmetry, the two-dimensional Sedov blast wave problem is studied to demonstrate the relation between the transverse flux and shock instability. Based on the theoretical analyses, a shock stable flux splitting scheme is presented through introducing additional viscosities of entropy wave and shear wave to damp out all perturbations in the transverse direction. For restoring the contact surface and shear layer, a pressure-based function depending on the shock-wave strength is defined to control the amount and location of additional viscosities. Numerical results of several challenging test problems demonstrate that the new scheme has greatly improved the robustness without undermining the accuracy.

在高超声速流的模拟中，低耗散冲击捕获方法通常会遭受各种形式的冲击不稳定性，例如臭名昭​​著的声现象。已经提出了许多解决通量差异分裂方案的冲击不稳定性的策略，例如HLLC和Roe方案，而针对通量分裂方案的冲击不稳定性所做的工作很少。在本文中，我们关注对流压力通量分裂方案的激波不稳定性。通过线性化扰动分析，结果表明，沿流向的所有扰动均被阻尼，而沿横向方向的密度和剪切速度的扰动未被阻尼。由于特殊的对称性 研究了二维Sedov爆炸波问题，以证明横向通量与激波不稳定性之间的关系。在理论分析的基础上，通过引入附加的熵波和切变粘度来抑制横向的所有扰动，提出了一种冲击稳定的磁通分裂方案。为了恢复接触表面和剪切层，定义了取决于冲击波强度的基于压力的功能来控制附加粘度的量和位置。几个具有挑战性的测试问题的数值结果表明，该新方案极大地提高了鲁棒性，而不会降低精度。通过引入附加的熵波和切变波粘度来消除横向上的所有扰动，提出了一种冲击稳定的磁通分裂方案。为了恢复接触表面和剪切层，定义了取决于冲击波强度的基于压力的功能来控制附加粘度的量和位置。几个具有挑战性的测试问题的数值结果表明，该新方案极大地提高了鲁棒性，而不会降低精度。通过引入附加的熵波和切变波粘度来消除横向上的所有扰动，提出了一种冲击稳定的磁通分裂方案。为了恢复接触表面和剪切层，定义了取决于冲击波强度的基于压力的功能来控制附加粘度的量和位置。几个具有挑战性的测试问题的数值结果表明，该新方案极大地提高了鲁棒性，而不会降低精度。