An effective preconditioning strategy for volume penalized incompressible/low Mach multiphase flow solvers
An effective preconditioning strategy for volume penalized incompressible/low Mach multiphase flow solvers
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DOI：
10.1016/j.jcp.2023.112325
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发表时间：
2023-06
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影响因子：
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通讯作者：
R. Thirumalaisamy;K. Khedkar;P. Ghysels;A. Bhalla
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作者：
R. Thirumalaisamy;K. Khedkar;P. Ghysels;A. Bhalla
体积惩罚法（VP）或Brinkman惩罚法（BP）是一种用于模拟海洋工程中多相流固耦合问题和热科学与工程中相变问题的扩散界面法。该方法依赖于惩罚因子（其与主体的渗透率κ成反比），该惩罚因子必须很大以在固体域中强制刚体速度。当惩罚因子较大时，离散方程组变得僵硬并且难以数值求解。本文提出了一种基于投影方法的预处理策略，用于求解体积惩罚（VP）不可压低马赫数Navier-Stokes方程。投影预处理器能够在单相（均匀密度和粘度）和多相（可变密度和粘度）流动设置中实现耦合速度-压力系统的整体解决方案。在这种方法中，惩罚力被隐式处理，这是允许采取任意大的值，而不影响求解器的收敛速度或导致数值刚度。这是可能的，包括惩罚项的压力泊松方程（PPE），这是不包括在以前的作品，解决VP不可压缩的Navier-Stokes方程使用投影方法。我们展示了如何和Brinkman惩罚项进入PPE重新推导投影算法的VP方法。求解器的可扩展性下的网格细化证明，即，无论问题大小如何，都可以用相同的迭代次数来实现收敛。在一个单一的阶段设置的制造解决方案是用来确定惩罚的解决方案的空间精度。考虑了体的渗透率κ的各种值。速度和压力的解决方案，为合理的小值的κ二阶逐点精度。当κ非常小时会出现误差饱和，但求解器的收敛速度不会降低。与先前的经验相反，随着κ减小，求解器收敛得更快。两个多相流体-结构相互作用（FSI）的问题，从海洋工程文献也进行了模拟，以评估求解器的鲁棒性和性能（在其迭代次数方面）。所提出的求解器还允许我们研究κ对浸没体表面上的接触线的运动的影响。它也使我们能够研究凝固金属自由表面的动力学。
The volume penalization (VP) or the Brinkman penalization (BP) method is a diffuse interface method for simulating multiphase fluid-structure interaction (FSI) problems in ocean engineering and/or phase change problems in thermal sciences and engineering. The method relies on a penalty factor (which is inversely related to body's permeabilityκ) that must be large to enforce rigid body velocity in the solid domain. When the penalty factor is large, the discrete system of equations becomes stiff and difficult to solve numerically. In this paper, we propose a projection method-based preconditioning strategy for solving volume penalized (VP) incompressible and low-Mach Navier-Stokes equations. The projection preconditioner enables the monolithic solution of the coupled velocity-pressure system in both single phase (uniform density and viscosity) and multiphase (variable density and viscosity) flow settings. In this approach, the penalty force is treated implicitly, which is allowed to take arbitrary large values without affecting the solver's convergence rate or causing numerical stiffness. It is made possible by including the penalty term in the pressure Poisson equation (PPE), which was not included in previous works that solved VP incompressible Navier-Stokes equations using the projection method. We show how and where the Brinkman penalty term enters the PPE by re-deriving the projection algorithm for the VP method. Solver scalability under grid refinement is demonstrated, i.e., convergence is achieved with the same number of iterations regardless of the problem size. A manufactured solution in a single phase setting is used to determine the spatial accuracy of the penalized solution. Various values of body's permeabilityκare considered. Second-order pointwise accuracy is achieved for both velocity and pressure solutions for reasonably small values ofκ. Error saturation occurs whenκis extremely small, but the convergence rate of the solver does not degrade. The solver converges faster asκdecreases, contrary to prior experience. Two multiphase fluid-structure interaction (FSI) problems from the ocean engineering literature are also simulated to evaluate the solver's robustness and performance (in terms of its number of iterations). The proposed solver also allows us to investigate the effect ofκon the motion of the contact line over the surface of the immersed body. It also allows us to investigate the dynamics of the free surface of a solidifying metal.