ABSTRACT A finite volume method based on the artificial compressibility scheme has been developed to simulate incompressible two-phase flows. In this method, the level set equation, used to capture the interface between two phases, is solved by coupling with the Navier-Stokes equations. The HLLC approximate Riemann solver, capable of resolving contact discontinuity accurately, is proposed to compute the intercell flux. In order to solve the interface flow accurately and efficiently, the high-order WENO reconstruction and the matrix-free implicit dual-time stepping method are applied in this study. Several classical cases, including a Rayleigh-Taylor instability problem, a broken dam problem and two bubble-rising problems are studied. The capability of the present scheme in simulating interface flows is validated by comparison with experimental data or reported results.

中文翻译：

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不可压缩两相流的一种HLLC型有限体积法

摘要 已经开发了一种基于人工可压缩性方案的有限体积方法来模拟不可压缩的两相流。在该方法中，用于捕获两相之间界面的水平集方程通过与 Navier-Stokes 方程耦合求解。HLLC近似黎曼求解器，能够准确地解决接触不连续性，被提出来计算胞间通量。为了准确高效地求解界面流动，本研究采用高阶WENO重构和无矩阵隐式双时间步进方法。研究了几个经典案例，包括瑞利-泰勒不稳定问题、破坝问题和两个气泡上升问题。