Abstract

The application of hybrid approximate Riemann solvers based on standard HLLC and HLL solvers is discussed. Three different hybrid solvers are considered. The first hybrid solver (rHLLC-HLL) uses a weighted sum of HLLC and HLL so that HLLC is applied in the direction normal to the shock wave, while HLL is applied in the direction along the wave. The second hybrid solver (HLLC-ADC) uses the weighted sum of HLLC and HLL, applying as weights the pressure function at the centers of the left and right cells. The third hybrid solver (HLLC-HLL) computes inviscid fluxes using HLL inside shock waves and HLLC in the other areas of the flow. The faces within the shock waves are determined by a shock-wave indicator based on the reconstructed pressure values to the left and to the right of the face. Several tests have been carried out showing that hybrid solvers prevent the emergence of carbuncle and reduce oscillations on shock waves.

中文翻译：

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基于HLLC和HLL的混合黎曼求解器在气体动力不连续流动模拟中的应用

摘要

讨论了基于标准HLLC和HLL求解器的混合近似黎曼求解器的应用。考虑了三种不同的混合求解器。第一个混合求解器 (rHLLC-HLL) 使用 HLLC 和 HLL 的加权和，以便 HLLC 应用于垂直于冲击波的方向，而 HLL 应用于沿波的方向。第二个混合求解器 (HLLC-ADC) 使用 HLLC 和 HLL 的加权和，应用左右单元中心的压力函数作为权重。第三个混合求解器 (HLLC-HLL) 使用冲击波内部的 HLL 和流动其他区域的 HLLC 来计算无粘通量。冲击波内的面由冲击波指示器根据面左侧和右侧的重建压力值来确定。多项测试表明，混合求解器可以防止痈的出现并减少冲击波的振荡。