A compressible two-fluid two-phase flow model based on two sets of governing equations is formulated. We solve, using the second-order Harten, Lax, and van Leer (HLL) scheme, five disparate two-phase benchmark problems such as shock propagation in the two-phase medium, the cavitating flow, and the gravity-induced phase separation. In the conventional HLL scheme, the simple sonic speeds evaluated from the two single phases are used in lieu of the fastest speeds in the two phases, since their accurate estimation is difficult. To improve the method, we here propose utilization of the analytic eigenvalues from the temporary 6 x 6 Jacobian matrix, reduced by dropping the interfacial transfer terms. The total sound speed of the two-phase flow evaluated by these eigenvalues agrees very well with the existing experimental data. The second-order HLL scheme using these analytic eigenvalues is proved efficient, robust, and accurate in comparison with other available methods.
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机译：建立了基于两组控制方程的可压缩两流体两相流模型。我们使用二阶Harten，Lax和van Leer（HLL）方案解决了五个不同的两相基准问题，例如两相介质中的激波传播，空化流以及重力引起的相分离。在传统的HLL方案中，由于难以精确估算，因此使用从两个单相评估的简单声速来代替两个相中的最快速度。为了改进该方法，我们在这里提出利用临时6 x 6雅可比矩阵的分析特征值，并通过除去界面转移项来减少该特征值。这些特征值评估的两相流的总声速与现有实验数据非常吻合。与其他可用方法相比，使用这些分析特征值的二阶HLL方案被证明是有效，稳健和准确的。
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