Computations of Single and Multiphase Flows Using a Lattice Boltzmann Solver

M. Akhtar, H. C. Love
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Abstract

There is considerable interest in high fidelity simulation of both single phase incompressible flows and multiphase flows. Most commonly applied numerical methods include finite difference, finite volume, finite element and spectral methods. All of these methods attempt to capture the flow details by solving the Navier–Stokes equations. Challenges of solving the Navier–Stokes single phase incompressible flows include the non-locality of the pressure gradient, non-linearity of the advection term and handling the pressure-velocity coupling. Multiphase flow computations pose additional challenges, such as property and flow variable discontinuities at the interface, whose location and orientation is not known a priori. Further, capturing/tracking of the multiphase interface requires solution of an additional advection equation. Recently, the lattice Boltzmann method has been applied to compute fluid dynamics simulations both for single and multiphase configurations; it is considered a modern CFD approach with improved accuracy and performance. Specifically, we employ a multiple-relaxation time (MRT) technique for the collision term on a D3Q27 lattice. The multiphase interface is captured using the phase-field approach of Allen-Cahn. Test cases include lid driven cavity, vortex shedding for a double backward facing step, Rayleigh Taylor instability, Enright’s deformation test and rising bubble in an infinite domain. These test cases validate different aspects of the single and multiphase model, so that the results can be interpreted with confidence that the underlying computational framework is sufficiently accurate.
用点阵玻尔兹曼解算器计算单相和多相流
对于单相不可压缩流和多相流的高保真度模拟有相当大的兴趣。最常用的数值方法有有限差分法、有限体积法、有限元法和谱法。所有这些方法都试图通过求解Navier-Stokes方程来捕捉流的细节。求解Navier-Stokes单相不可压缩流的挑战包括压力梯度的非局域性、平流项的非线性和压力-速度耦合的处理。多相流计算带来了额外的挑战,例如在界面处的性质和流动变量不连续,其位置和方向是未知的。此外,捕获/跟踪多相界面需要解一个额外的平流方程。近年来,晶格玻尔兹曼方法已被应用于计算单相和多相结构的流体动力学模拟;它被认为是一种具有更高精度和性能的现代CFD方法。具体来说,我们对D3Q27晶格上的碰撞项采用了多重弛豫时间(MRT)技术。采用Allen-Cahn相场法捕获多相界面。试验用例包括盖驱动空腔、双后台阶涡脱落、瑞利-泰勒失稳、恩莱特变形试验和无限域上升气泡。这些测试用例验证了单阶段和多阶段模型的不同方面,因此可以对结果进行解释,并确信底层的计算框架是足够准确的。
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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