In this work, a lattice Boltzmann (LB) model based on the phase-field method is proposed for simulating large density ratio two-phase flows. An improved multiple-relaxation-time (MRT) LB equation is first developed to solve the conserved Allen-Cahn (AC) equation. By utilizing a nondiagonal relaxation matrix and modifying the equilibrium distribution function and discrete source term, the conserved AC equation can be correctly recovered by the proposed MRT LB equation with no deviation term. Therefore, the calculations of the temporal derivative term in the previous LB models are successfully avoided. Numerical tests demonstrate that satisfactory accuracy can be achieved by the present model to solve the conserved AC equation. What is more, the discrete force term of the MRT LB equation for the incompressible Navier-Stokes equations is also simplified and modified in the present work. An alternative scheme to calculate the gradient terms of the order parameter involved in the discrete force term through the nonequilibrium part of the distribution function is also developed. To validate the ability of the present LB model for simulating large density ratio two-phase flows, series of benchmarks, including two-phase Poiseuille flow, droplet impacting on thin liquid film, and planar Taylor bubble are simulated. It is found that the results predicted by the present LB model agree well with the analytical, numerical, and experimental results.

中文翻译：

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大密度比两相流的相场格子玻尔兹曼模型

在这项工作中，提出了一种基于相场法的格子玻尔兹曼（LB）模型来模拟大密度比两相流。首先开发了一种改进的多重弛豫时间 (MRT) LB 方程来求解守恒的 Allen-Cahn (AC) 方程。通过利用非对角松弛矩阵并修改平衡分布函数和离散源项，可以通过所提出的 MRT LB 方程正确恢复守恒的 AC 方程，而没有偏差项。因此，成功地避免了之前 LB 模型中时间导数项的计算。数值试验表明，本模型求解守恒AC方程可以达到令人满意的精度。更，不可压缩的 Navier-Stokes 方程的 MRT LB 方程的离散力项也在本工作中进行了简化和修改。还开发了一种通过分布函数的非平衡部分计算离散力项中涉及的阶参数梯度项的替代方案。为验证现有 LB 模型模拟大密度比两相流的能力，对包括两相泊肃叶流、液滴撞击薄液膜和平面泰勒气泡在内的一系列基准进行了模拟。结果表明，本 LB 模型预测的结果与解析、数值和实验结果吻合良好。还开发了一种通过分布函数的非平衡部分计算离散力项中涉及的阶参数梯度项的替代方案。为验证现有 LB 模型模拟大密度比两相流的能力，对包括两相泊肃叶流、液滴撞击薄液膜和平面泰勒气泡在内的一系列基准进行了模拟。结果表明，本 LB 模型预测的结果与解析、数值和实验结果吻合良好。还开发了一种通过分布函数的非平衡部分计算离散力项中涉及的阶参数梯度项的替代方案。为验证现有 LB 模型模拟大密度比两相流的能力，对包括两相泊肃叶流、液滴撞击薄液膜和平面泰勒气泡在内的一系列基准进行了模拟。结果表明，本 LB 模型预测的结果与解析、数值和实验结果吻合良好。和平面泰勒气泡进行模拟。结果表明，本 LB 模型预测的结果与解析、数值和实验结果吻合良好。和平面泰勒气泡进行模拟。结果表明，本 LB 模型预测的结果与解析、数值和实验结果吻合良好。