一种稳健的全马赫数六方程扩散界面多相流方法（含表面张力）
A Robust All-Mach Six-Equation Diffuse-Interface Method for Multiphase Flows with Surface Tension
- Indian Institute of Technology Bombay（印度理工学院孟买分校）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
提出一种稳健的全马赫数六方程扩散界面方法，结合HLLC求解器和低马赫数修正，准确模拟含表面张力的可压缩多相流，显著降低数值耗散并保持稳定性。
AI中文摘要：
本文提出了一种稳健的有限体积框架，用于模拟在宽马赫数范围内具有表面张力的可压缩多相流。该方法基于双压力、六方程扩散界面模型，通过连续表面力公式纳入粘性、重力和毛细效应。为一致地考虑毛细引起的压力跳跃，利用广义黎曼不变量分析开发了HLLC黎曼求解器，并修改了瞬时压力松弛过程，以在相平衡期间保持拉普拉斯压力跳跃。为克服传统近似黎曼求解器在低马赫数 regime 下的过度数值扩散，通过扩展我们之前的公式并提出一种改进的缩放策略，提出了一种稳健的低马赫数修正，该策略在强压力变化区域保持稳定。所提出的方法在从几乎不可压缩流动到可压缩 regime 的范围内保持精度，同时保持六方程公式的稳健性。该数值框架通过一系列涉及表面张力、粘性、重力和可压缩性的基准问题进行验证。结果表明，该方法能准确预测界面动力学、毛细压力和低马赫数流动特征，同时显著减少数值耗散而不损害稳定性。所提出的方法为模拟涵盖广泛流动 regime 的复杂多相流提供了一种高效且可靠的方法。
英文摘要：
A robust finite-volume framework is presented for the simulation of compressible multiphase flows with surface tension across a wide range of Mach numbers. The method is based on a two-pressure, six-equation diffuse interface model incorporating viscous, gravitational, and capillary effects through the continuum surface force formulation. To consistently account for capillary-induced pressure jumps, an HLLC Riemann solver is developed using generalized Riemann invariant analysis, and the instantaneous pressure relaxation procedure is modified to preserve the Laplace pressure jump during phase equilibration. To overcome the excessive numerical diffusion of conventional approximate Riemann solvers in the low-Mach regime, a robust low-Mach correction is proposed by extending our previous formulation with a modified scaling strategy that remains stable in regions of strong pressure variation. The resulting method retains accuracy from nearly incompressible flows to compressible regimes while preserving the robustness of the six-equation formulation. The numerical framework is validated using a series of benchmark problems involving surface tension, viscosity, gravity, and compressibility. The results demonstrate accurate prediction of interface dynamics, capillary pressure, and low-Mach flow features, while significantly reducing numerical dissipation without compromising stability. The proposed methodology provides an efficient and reliable approach for the simulation of complex multiphase flows spanning a broad range of flow regimes.
