A mixed upwind/central WENO scheme for incompressible two-phase flows
A mixed upwind/central WENO scheme for incompressible two-phase flows
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DOI：
10.1016/j.jcp.2019.02.043
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发表时间：
2019-06
期刊：
影响因子：
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通讯作者：
Ziyang Huang;G. Lin;A. Ardekani
中科院分区：
文献类型：
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作者：
Ziyang Huang;G. Lin;A. Ardekani
本文发展了一种精确、高效的数值格式来求解具有守恒形式非线性惯性项的两相流Navier-Stokes方程。两相流中守恒形式的非线性惯性项的离散化的主要困难在于跨界面动量的不连续性。为了克服这个困难，我们开发了混合迎风/中央韦诺格式，使没有网格变形或映射，或显式界面重建是必要的。我们的混合逆风/中央韦诺计划还消除了对接口跟踪/捕获方法的依赖，因此它与任何流行的接口跟踪/捕获方法兼容。为了解耦两相系统的整体方程，构造了一种高效的半隐式投影格式，该格式既保留了压力稳定法的效率，又对机器精度施加了无发散条件，有利于界面对流、约化一致性和大密度比。数值实验验证了该投影格式的精度和降阶一致性。几个基准的情况下，执行显示的能力，整体计划处理现实的两相问题，多个物理效应，复杂的界面演变和/或大密度比（ρ水/ρ空气）的顺序。定量和定性的比较已经取得了很好的协议与解析解，发表的数值和/或实验结果。
In this paper, an accurate and efficient numerical scheme is developed to solve the Navier-Stokes equations for two-phase flow systems with the nonlinear inertial term in conservation form. The major difficulty of discretizing the nonlinear inertial term in conservation form in two-phase flows is rooted in the discontinuous nature of momentum across interfaces. To overcome this difficulty, we developed the mixed Upwind/Central WENO scheme so that no grid deformation or mapping, or explicit interface reconstruction is necessary. Our mixed Upwind/Central WENO scheme also removes the dependence on the interface tracking/capturing method so it is compatible with any popular interface tracking/capturing methods. To decouple the overall equations of the two-phase system, an efficient semi-implicit projection scheme is constructed, which shares the efficiency of pressure stabilization method while enforces divergence-free condition to machine precision, to benefit interface advection, reduction consistency as well as large density ratio. The accuracy and reduction consistency of this projection scheme are validated by numerical experiments. Several benchmark cases are performed to show the capability of the overall scheme handling realistic two-phase problems with multiple physical effects, complex interface evolution and/or large density ratio of the order of (ρ water/ρ air). Both quantitative and qualitative comparisons have been made and very good agreements with analytical solutions, published numerical and/or experimental results are achieved.