Simulating two-phase flows with thermodynamically consistent energy stable Cahn-Hilliard Navier-Stokes equations on parallel adaptive octree based meshes
Simulating two-phase flows with thermodynamically consistent energy stable Cahn-Hilliard Navier-Stokes equations on parallel adaptive octree based meshes
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DOI：
10.1016/j.jcp.2020.109674
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发表时间：
2019-12
期刊：
影响因子：
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通讯作者：
Makrand A. Khanwale;Alec Lofquist;H. Sundar;J. Rossmanith;B. Ganapathysubramanian
中科院分区：
文献类型：
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作者：
Makrand A. Khanwale;Alec Lofquist;H. Sundar;J. Rossmanith;B. Ganapathysubramanian
通过求解热力学相容的Cahn-Hilliard Navier-Stokes方程，对不同密度差下具有变形界面的两相流动进行了模拟。采用(本质上)无条件能量稳定的Crank-Nicolson型时间积分格式。给出了半离散格式的能量稳定性和对流扩散Cahn-Hilliard算子解的存在性的详细证明。我们用协调的连续伽辽金有限元方法和基于残差的变分多尺度(VMS)方法来离散空间项，以提供压力稳定。我们使用基于快速八叉树的自适应网格将该方法部署在大规模并行数值实现上。对求解器进行了详细的标度分析。对于较大的密度比范围，给出了收敛的数值实验，并与文献中的实验结果进行了验证。
We report on simulations of two-phase flows with deforming interfaces at various density contrasts by solving thermodynamically consistent Cahn-Hilliard Navier-Stokes equations. An (essentially) unconditionally energy-stable Crank-Nicolson-type time integration scheme is used. Detailed proofs of energy stability of the semi-discrete scheme and for the existence of solutions of the advective-diffusive Cahn-Hilliard operator are provided. We discretize spatial terms with a conforming continuous Galerkin finite element method in conjunction with a residual-based variational multi-scale (VMS) approach in order to provide pressure stabilization. We deploy this approach on a massively parallel numerical implementation using fast octree-based adaptive meshes. A detailed scaling analysis of the solver is presented. Numerical experiments showing convergence and validation with experimental results from the literature are presented for a large range of density ratios.