A projection-based, semi-implicit time-stepping approach for the Cahn-Hilliard Navier-Stokes equations on adaptive octree meshes
A projection-based, semi-implicit time-stepping approach for the Cahn-Hilliard Navier-Stokes equations on adaptive octree meshes
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DOI：
10.1016/j.jcp.2022.111874
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发表时间：
2021-07
期刊：
影响因子：
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通讯作者：
Makrand A. Khanwale;K. Saurabh;Masado Ishii;H. Sundar;J. Rossmanith;Baskar-Ganapathysubramanian
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文献类型：
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作者：
Makrand A. Khanwale;K. Saurabh;Masado Ishii;H. Sundar;J. Rossmanith;Baskar-Ganapathysubramanian
Cahn-Hilliard Navier-Stokes(CHNS)系统提供了一个易于计算的模型，可以用来有效地捕捉两相流体流动中的界面动力学。在这项工作中，我们提出了一个半隐式的，基于投影的有限元框架来求解CHNS系统。我们对Navier-Stokes方程采用了基于投影的半隐式时间离散，对Cahn-Hilliard方程采用了全隐式时间离散。我们在空间中使用协调连续Galerkin(CG)有限元方法，并配备了基于残差的变分多尺度(RBVMS)格式。用投影步长解耦压力，得到速度和压力的两个线性半正定系统，而不是稳压方法中的鞍点系统。所有的线性方程组都使用了一种高效的、可伸缩的代数多重网格(AMG)方法。我们使用基于并行八叉树的自适应网格将该方法应用于大规模并行数值实现。整体方法允许使用相对较大的时间步长，比类似的完全隐式方法具有更快的求解时间。我们给出了全面的数值实验，与文献中典型情况的结果进行了详细的比较，包括单个气泡上升和Rayleigh-Taylor不稳定性。
The Cahn-Hilliard Navier-Stokes (CHNS) system provides a computationally tractable model that can be used to effectively capture interfacial dynamics in two-phase fluid flows. In this work we present a semi-implicit, projection-based finite element framework for solving the CHNS system. We use a projection-based semi-implicit time discretization for the Navier-Stokes equation and a fully-implicit time discretization for the Cahn-Hilliard equation. We use a conforming continuous Galerkin (cG) finite element method in space equipped with a residual-based variational multiscale (RBVMS) formulation. Pressure is decoupled using a projection step, which results in two linear positive semi-definite systems for velocity and pressure, instead of the saddle point system of a pressure-stabilized method. All the linear systems are solved using an efficient and scalable algebraic multigrid (AMG) method. We deploy this approach on a massively parallel numerical implementation using parallel octree-based adaptive meshes. The overall approach allows the use of relatively large time steps with much faster time-to-solve than similar fully-implicit methods. We present comprehensive numerical experiments showing detailed comparisons with results from the literature for canonical cases, including the single bubble rise and Rayleigh-Taylor instability.