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首页> 外文期刊>Journal of Computational Physics >Central moment lattice Boltzmann method using a pressure-based formulation for multiphase flows at high density ratios and including effects of surface tension and Marangoni stresses
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Central moment lattice Boltzmann method using a pressure-based formulation for multiphase flows at high density ratios and including effects of surface tension and Marangoni stresses

机译：中央一轮晶格玻璃螺柱方法，使用基于压力的多相形式的高密度比率，包括表面张力和Marangoni应力的影响

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摘要

Simulation of multiphase flows, which are ubiquitous in nature and engineering applications, require coupled capturing or tracking of the interfaces in conjunction with the solution of fluid motion often occurring at multiple scales. In this contribution, we will present unified cascaded LB methods based on central moments for the solution of the incompressible two-phase flows at high density ratios and for capturing of the interfacial dynamics. Based on a modified continuous Boltzmann equation (MCBE) for two-phase flows, where a kinetic transformation to the distribution function involving the pressure field is introduced to reduce the associated numerical stiffness at high density gradients, a central moment cascaded LB formulation using multiple relaxation times for computing the fluid motion will be constructed. In this LB scheme, the collision step is prescribed by the relaxation of various central moments to their equilibria that are reformulated in terms of the pressure field obtained via matching to the continuous equilibria based on the transformed Maxwell distribution. Furthermore, the differential treatments for the effects of the source term representing the change due to the pressure field and of the source term due to the interfacial tension force and body forces appearing in the MCBE on different moments are consistently accounted for in this cascaded LB solver that computes the pressure and velocity fields. In addition, another cascaded LB scheme will be developed to solve for the interfacial dynamics represented by a phase field model based on the conservative Allen-Cahn equation that evolves interfaces by advection and under the competing effects due to a diffusion term and a phase segregation flux term. The latter is introduced into the cascaded LB scheme via a modification to the moment equilibria. Based on numerical simulations of a variety of two-phase flow benchmark problems at high density ratios and involving the effects of surface tension and its tangential gradients (Marangoni stresses), we will validate our unified cascaded LB approach and also demonstrate improvements in numerical stability. (C) 2020 Elsevier Inc. All rights reserved.
机译：多相流的模拟在自然界和工程应用中普遍存在，需要对界面进行耦合捕获或跟踪，并结合在多个尺度上经常发生的流体运动的解决方案。在本文中，我们将介绍基于中心矩的统一级联LB方法，用于求解高密度比下的不可压缩两相流，并用于捕捉界面动力学。基于修正的两相流连续玻尔兹曼方程（MCBE），其中引入了涉及压力场的分布函数的动力学变换，以降低高密度梯度下的相关数值刚度，将构造一个使用多次松弛时间计算流体运动的中心力矩级联LB公式。在这种LB格式中，碰撞步骤是通过将各种中心力矩松弛到它们的平衡点来规定的，这些平衡点是根据根据变换后的麦克斯韦分布匹配到连续平衡点而获得的压力场重新表示的。此外，在这个计算压力场和速度场的级联LB解算器中，始终考虑了源项（表示压力场引起的变化）和源项（表示MCBE中不同时刻出现的界面张力和体力引起的变化）效应的差异处理。此外，还将开发另一个级联LB方案，以解决由基于保守Allen-Cahn方程的相场模型表示的界面动力学问题，该方程通过平流和在扩散项和相分离通量项的竞争效应下演化界面。后者通过对力矩平衡的修正被引入到级联LB格式中。基于高密度比下各种两相流基准问题的数值模拟，以及表面张力及其切向梯度（Marangoni应力）的影响，我们将验证我们的统一级联LB方法，并展示数值稳定性的改进。（C） 2020爱思唯尔公司版权所有。

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