Study of phase-field lattice Boltzmann models based on the conservative Allen-Cahn equation
Study of phase-field lattice Boltzmann models based on the conservative Allen-Cahn equation
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DOI：
10.1103/physreve.102.023305
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发表时间：
2020-08-12
影响因子：
2.4
通讯作者：
Bolster, Diogo
中科院分区：
文献类型：
--
作者：
Begmohammadi, Amirhosein;Haghani-Hassan-Abadi, Reza;Bolster, Diogo
基于Allen-Cahn模型的守恒相场（CPF）方程在多相流中的界面跟踪近年来变得越来越流行，特别是在格子Boltzmann（LB）社区中。这在很大程度上是由于他们的简单性和提高效率和准确性比他们的凯恩-希利亚德为基础的同行。此外，所得到的LB方程（LBE）的CPF模型的改进的局部性，使他们更理想的候选人LB模拟多相流的非均匀网格，特别是在自适应网格细化框架和大规模并行实现。在这方面，Geier等人[Phys. Rev. E 91，063309（2015）]对原始CPF-LBE进行了一些修改（旨在改进），需要进一步检查。本研究的目的是对Geier等人提出的原始CPF模型[Phys.Rev.E91，063309（2015）]与Ren等人提出的所谓改进[Phys.Rev.E94，023311（2016）]和Wang等人[Phys.Rev.E94，033304（2016）]。使用Chapman-Enskog分析，我们提供了一个详细的推导每个模型中的控制方程，然后检查上述模型的一些基准问题的有效性。已经设计了几个测试用例来研究不同的配置，从基本的信息流到更复杂的流场，并将结果与有限差分模拟进行比较。此外，作为先前提出的CPF-LBE模型的发展，Geier等人[Phys. Rev. E 91，063309（2015）]提出的模型的轴对称公式被推导和呈现。最后，设计了两个基准问题来比较所提出的轴对称模型与解析解和以前的工作。我们发现，在高粘度比，高密度比，和相对较高的雷诺数不同的模型，界面跟踪模型的准确性大致相似，而原始CFP-LBE没有额外的时间依赖项优于所谓的改进模型的效率，特别是在分布式并行机。
Conservative phase-field (CPF) equations based on the Allen-Cahn model for interface tracking in multiphase flows have become more popular in recent years, especially in the lattice-Boltzmann (LB) community. This is largely due to their simplicity and improved efficiency and accuracy over their Cahn-Hilliard-based counterparts. Additionally, the improved locality of the resulting LB equation (LBE) for the CPF models makes them more ideal candidates for LB simulation of multiphase flows on nonuniform grids, particularly within an adaptive-mesh refinement framework and massively parallel implementation. In this regard, some modifications-intended as improvements-have been made to the original CPF-LBE proposed by Geier et al. [Phys. Rev. E 91, 063309 (2015)] which require further examination. The goal of the present study is to conduct a comparative investigation into the differences between the original CPF model proposed by Geier et al. [Phys. Rev. E 91, 063309 (2015)] and the so-called improvements proposed by Ren et al. [Phys. Rev. E 94, 023311 (2016)] and Wang et al. [Phys. Rev. E 94, 033304 (2016)]. Using the Chapman-Enskog analysis, we provide a detailed derivation of the governing equations in each model and then examine the efficacy of the above-mentioned models for some benchmark problems. Several test cases have been designed to study different configurations ranging from basic yet informative flows to more complex flow fields, and the results are compared with finite-difference simulations. Furthermore, as a development of the previously proposed CPF-LBE model, axisymmetric formulations for the proposed model by Geier et al. [Phys. Rev. E 91, 063309 (2015)] are derived and presented. Finally, two benchmark problems are designed to compare the proposed axisymmetric model with the analytical solution and previous work. We find that the accuracy of the model for interface tracking is roughly similar for different models at high viscosity ratios, high density ratios, and relatively high Reynolds numbers, while the original CFP-LBE without the additional time-dependent terms outperforms the so-called improved models in terms of efficiency, particularly on distributed parallel machines.