In this paper, the Allen-Cahn-Multiphase lattice Boltzmann flux solver (AC-MLBFS) is proposed as a new and effective numerical simulation method for multiphase flows with high density ratios. The MLBFS resolves the macroscopic governing equations with the finite volume method and reconstructs numerical fluxes on the cell interface from local solutions to the lattice Boltzmann equation, which combines the advantages of conventional Navier–Stokes solvers and lattice Boltzmann methods for simulating incompressible multiphase flows while alleviating their limitations. Previous MLBFS-based multiphase solvers performed poorly in mass conservation, which might be caused by the excessive numerical diffusion in the Cahn-Hilliard (CH) model used as the interface tracking algorithm. To resolve this problem, the present method proposes using the conservative Allen-Cahn (AC) model as the interfacial tracking algorithm, which can ease the numerical implementation by removing high order derivative terms and alleviate mass leakage by enforcing local mass conservation in the physical model. Numerical validations will be carried out through benchmark tests at high density ratios and in extreme conditions with large Reynolds or Weber numbers. Through these examples, the accuracy and robustness as well as the mass conservation characteristics of the proposed method are demonstrated.

中文翻译：

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具有保守 Allen-Cahn 模型的多相晶格玻尔兹曼通量求解器，用于模拟高密度比流

在本文中，艾伦-卡恩多相格子玻尔兹曼通量求解器（AC-MLBFS）被提出作为一种新的有效的高密度比多相流数值模拟方法。 MLBFS采用有限体积法求解宏观控制方程，并将单元界面上的数值通量从局部解重构为格子Boltzmann方程，它结合了传统Navier-Stokes求解器和格子Boltzmann方法的优点，可以模拟不可压缩多相流，同时减轻他们的局限性。之前基于 MLBFS 的多相求解器在质量守恒方面表现不佳，这可能是由于用作界面跟踪算法的 Cahn-Hilliard (CH) 模型中过度数值扩散造成的。为了解决这个问题，本方法提出使用保守的 Allen-Cahn (AC) 模型作为界面跟踪算法，它可以通过删除高阶导数项来简化数值实现，并通过在物理模型中强制执行局部质量守恒来减轻质量泄漏。数值验证将通过高密度比和极端条件下具有大雷诺数或韦伯数的基准测试进行。通过这些例子，证明了所提出方法的准确性和鲁棒性以及质量守恒特性。