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
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
复制标题
DOI：
10.1016/j.jcp.2020.109893
复制
发表时间：
2019-09
期刊：
影响因子：
--
通讯作者：
Farzaneh Hajabdollahi;K. Premnath;S. Welch
中科院分区：
文献类型：
--
作者：
Farzaneh Hajabdollahi;K. Premnath;S. Welch
在自然界和工程应用中普遍存在的多相流的模拟需要结合经常发生在多个尺度上的流体运动的解决方案来耦合捕获或跟踪界面。在这方面的贡献，我们将提出统一的级联LB方法的基础上的中心矩的解决方案的不可压缩两相流在高密度比和捕获的界面动力学。基于一个修改的连续玻尔兹曼方程（MCBE）的两相流，其中的动力学变换的分布函数，包括压力场被引入到减少相关的数值刚度在高密度梯度，中心矩级联LB配方使用多个松弛时间计算流体运动将被构造。在这个LB计划中，规定的碰撞步骤的各种中心时刻的放松，以他们的平衡，重新制定的压力场，通过匹配的基础上变换的麦克斯韦分布的连续平衡。此外，差分处理的源项表示的变化，由于压力场和源项由于界面张力和体力出现在MCBE上的不同时刻的影响是一致的占在这个级联LB求解器，计算压力和速度场。此外，另一个级联LB计划将被开发，以解决由相场模型表示的界面动力学的基础上的保守的艾伦-卡恩方程，演变界面的平流和竞争的影响下，由于扩散项和相分离通量项。后者被引入到级联LB计划通过修改的时刻平衡。基于高密度比的各种两相流基准问题的数值模拟，并涉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，并证明数值稳定性的改善。
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.