Lattice Boltzmann framework for multiphase flows by Eulerian-Eulerian Navier-Stokes equations

Matteo Maria Piredda, Pietro Asinari
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Abstract

Although Lattice Boltzmann Method (LBM) is relatively straightforward, it demands a well-crafted framework to handle the complex partial differential equations involved in multiphase flow simulations. This document presents some potential strategies for developing an Eulerian-Eulerian LBM solver tailored for multiphase systems. The paper first states what are the starting equations governing a multiphase flow in classical CFD. Secondly, it derives a pseudo-compressible (targeting the incompressible limit) system of equations for deriving the Eulerian-Eulerian LBM framework to simulate multiphase flows. Finally, a dispersed phase volume fraction equation is provided to balance the degree of freedom less due to the pressure gradient coupling. The effectiveness of these approaches can only be confirmed through rigorous numerical experimentation.
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通过欧拉-欧拉纳维-斯托克斯方程实现多相流的晶格玻尔兹曼框架
尽管晶格玻尔兹曼法(LBM)相对简单,但它需要一个精心设计的框架来处理多相流模拟中涉及的复杂偏微分方程。本文介绍了开发适合多相系统的欧拉-欧拉 LBM 求解器的一些潜在策略。本文首先阐述了经典 CFD 中多相流的起始方程。最后,提供了一个分散相体积分数方程,以平衡因压力梯度耦合而减少的自由度。只有通过严格的数值实验才能证实这些方法的有效性。
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