In this work, the Harten-Lax-van Leer Contact (HLLC) approximate Riemann solver is extended to two-phase flow through ducts with discontinuous cross-sections. Two main strategies are explored regarding the treatment of the non-conservative term arising in the governing equations. In the first, labelled HLLC+S, the non-conservative term is discretized separately. In the second, labelled HLLCS, the non-conservative term is incorporated in the Riemann solver. The methods are assessed by numerical tests for single and two-phase flow of CO${}_2$, the latter employing a homogeneous equilibrium model where the thermodynamic properties are calculated using the Peng–Robinson equation of state. The methods have different strengths, but in general, HLLCS is found to work best. In particular, it is demonstrated to be equally accurate and more robust than existing methods for non-resonant flow. It is also well-balanced for subsonic flow in the sense that it conserves steady-state flow.

在这项工作中，Harten-Lax-van Leer Contact (HLLC) 近似黎曼求解器被扩展到通过具有不连续横截面的管道的两相流。关于处理控制方程中出现的非保守项，探索了两种主要策略。在第一个标记为 HLLC+S 中，非保守项被单独离散化。在第二个标记为 HLLCS 的情况下，非保守项包含在黎曼求解器中。这些方法通过对 CO 单相和两相流的数值试验进行评估${}_2$，后者采用均匀平衡模型，其中使用 Peng-Robinson 状态方程计算热力学性质。这些方法具有不同的优势，但总的来说，发现 HLLCS 效果最好。特别是，它被证明与非共振流的现有方法同样准确且更稳健。从它保存稳态流动的意义上说，它对于亚音速流动也是很好的平衡。