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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:425

Article; Proceedings Paper

Hajabdollahi, Farzaneh¹  Premnath, Kannan N.¹  Welch, Samuel W. J.¹ 

[1] Univ Colorado, Dept Mech Engn, 1200 Larimer St, Denver, CO 80217 USA

关键词: Lattice Boltzmann method;    Central moments;    Multiphase flows;    Surface tension;    Phase-field model;   

DOI  :  10.1016/j.jcp.2020.109893

来源: Elsevier

【 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.

【 授权许可】

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