Consistent multiple-relaxation-time lattice Boltzmann method for the volume-averaged Navier-Stokes equations

IF 3.8 2区物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal of Computational Physics Pub Date : 2025-09-16 DOI:10.1016/j.jcp.2025.114379

Yang Liu , Xuan Zhang , Jingchun Min , Xiaomin Wu

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引用次数: 0

Abstract

The volume-averaged Navier-Stokes equations (VANSE), serving as the cornerstone of various fluid-solid multiphase models, have recently been reported to be solved using a pressure-based lattice Boltzmann (LB) method that decouples the pressure from density and exhibits good numerical performance [1]. However, the widely adopted density-based LB scheme still suffers from significant spurious velocities and inconsistency with VANSE. To remedy this issue, this paper introduces a multiple-relaxation-time LB method, which incorporates a provisional equation of state into the redefined equilibrium distribution to decouple the void fraction from density, and readjusts a correction force to produce correct pressure term. Also, Galilean invariance of the recovered VANSE is guaranteed by devising a source term in moment space, effectively eliminating unwanted numerical errors in viscous stress tensor. Through Chapman-Enskog analysis and comprehensive numerical validations, this proposed scheme is demonstrated to be capable of recovering consistent VANSE with second-order accuracy, and offers better numerical stability over previous schemes for handling void fraction fields with large gradients and spatiotemporal distributions.

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体积平均Navier-Stokes方程的一致多重松弛时间晶格Boltzmann方法

体积平均Navier-Stokes方程（VANSE）作为各种流固多相模型的基础，最近被报道使用基于压力的晶格Boltzmann （LB）方法求解，该方法将压力与密度解耦，并显示出良好的数值性能[1]。然而，广泛采用的基于密度的LB方案仍然存在明显的伪速度和与VANSE不一致的问题。为了解决这一问题，本文引入了一种多松弛时间LB方法，该方法将临时状态方程纳入重新定义的平衡分布中，以解耦空隙率和密度，并重新调整修正力以产生正确的压力项。此外，通过在矩空间中设计源项来保证恢复VANSE的伽利略不变性，有效地消除了粘性应力张量中不必要的数值误差。通过Chapman-Enskog分析和综合数值验证，该方案能够以二阶精度恢复一致的VANSE，并且在处理具有大梯度和时空分布的孔隙分数场时，比以前的方案具有更好的数值稳定性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Computational Physics 物理-计算机：跨学科应用

CiteScore

7.60

自引率

14.60%

发文量

763

审稿时长

5.8 months

期刊介绍： Journal of Computational Physics thoroughly treats the computational aspects of physical problems, presenting techniques for the numerical solution of mathematical equations arising in all areas of physics. The journal seeks to emphasize methods that cross disciplinary boundaries. The Journal of Computational Physics also publishes short notes of 4 pages or less (including figures, tables, and references but excluding title pages). Letters to the Editor commenting on articles already published in this Journal will also be considered. Neither notes nor letters should have an abstract.