Abstract We propose an interface-sharpening method for volume-of-fluid simulations of two-phase compressible flows. In the proposed method, sharpening of the interface between two phases is achieved by introducing a source term to the advection-reaction equation for the phase volume fraction. The inherent numerical diffusivity arising from the discretization of this equation is used to construct the source term. The resulting governing equations of the two-phase compressible flow are quasi-conservative and hyperbolic, with the phase volume fraction being bounded and free of spurious oscillations. The proposed method, called advection-reaction interface sharpening (ARIS), can be applied inline so that no post-processing of the phase volume fraction is required after each time step. The conservation equations for mass, momentum and energy are solved with a dimensional-splitting Monotone Upstream-centered Scheme for Conservation Laws (MUSCL). The interfacial resolution is improved by combining a fully-threaded-tree algorithm with adaptive mesh refinement. In validation tests performed on a variety of one- and two-dimensional benchmark flows, we find that ARIS can reduce the interface thickness to just three to four computational cells, improving the interfacial resolution without sacrificing computational efficiency. This study shows that ARIS can provide robust, quasi-conservative, oscillation-free and nearly sharp solutions of the phase volume fraction in various one- and two-dimensional interfacial flows, paving the way for extensions of this method to three-dimensional flows with more than two phases.

中文翻译：

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用于两相可压缩流的流体体积模拟的自适应网格细化界面锐化方法

摘要 我们提出了一种用于两相可压缩流动的流体体积模拟的界面锐化方法。在所提出的方法中，通过在相体积分数的平流反应方程中引入源项来实现两相之间界面的锐化。由该方程的离散化产生的固有数值扩散率用于构造源项。得到的两相可压缩流的控制方程是准守恒和双曲线的，相体积分数有界且没有虚假振荡。所提出的方法称为对流反应界面锐化 (ARIS)，可以在线应用，因此在每个时间步长之后不需要对相体积分数进行后处理。质量守恒方程，动量和能量通过维数分裂单调上游中心守恒定律方案 (MUSCL) 解决。通过将全线程树算法与自适应网格细化相结合，可以提高界面分辨率。在对各种一维和二维基准流进行的验证测试中，我们发现 ARIS 可以将界面厚度减少到三到四个计算单元，在不牺牲计算效率的情况下提高界面分辨率。这项研究表明，ARIS 可以提供各种一维和二维界面流中相体积分数的稳健、准保守、无振荡和近乎尖锐的解，为将该方法扩展到三维流动铺平了道路两个以上的阶段。