A simplified lattice Boltzmann flux solver for multiphase flows with large density ratio,International Journal for Numerical Methods in Fluids

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A simplified lattice Boltzmann flux solver for multiphase flows with large density ratio
International Journal for Numerical Methods in Fluids ( IF 1.7 ) Pub Date : 2021-01-15 , DOI: 10.1002/fld.4958
Liuming Yang _{1,

2} , Chang Shu ₂ , Zhen Chen _{2,

3} , Yan Wang ₄ , Guoxiang Hou ₁

Affiliation

Unlike the conventional multiphase lattice Boltzmann method (LBM), the recently developed finite volume‐based multiphase lattice Boltzmann flux solver (MLBFS) is free from the limitation of the uniform mesh, the coupled time step and mesh spacing, and the high virtual memories. In the MLBFS, the macroscopic equations recovered from the LBM are discretized by the finite volume method while the fluxes at the cell interfaces are evaluated based on the local application of LBM. The interfacial fluxes are calculated only by the distribution functions. However, the code implementation involving too many distribution functions is still not simple enough. And the computation of the distribution functions will still cost relatively large computational resources. We notice that some moments of the distribution functions can be directly simplified as the macroscopic variables. Therefore, to further simplify the code implementation and improve the computational efficiency of the MLBFS, we propose a simplified MLBFS which reconstructs the fluxes with the combination of the distribution functions and the macroscopic variables. Naturally, we can expect that the simplified method can improve the computational efficiency while maintaining the numerical accuracy and reliability of the original MLBFS. Numerical experiments of the Laplace law, the Rayleigh–Taylor instability, the bubble rising under buoyancy and the droplet splashing on a liquid film are conducted to evaluate the simplified MLBFS. Results show that our method can save up to 18.32% of the original computational time. The simplified method is superior to the original one especially for the cases with a large number of girds.

中文翻译：

简化的大密度比多相流格子Boltzmann通量求解器

与传统的多相格子Boltzmann方法（LBM）不同，最近开发的基于有限体积的多相格子Boltzmann通量求解器（MLBFS）不受均匀网格，耦合时间步长和网格间距以及高虚拟内存的限制。在MLBFS中，从LBM恢复的宏观方程式通过有限体积法离散化，同时基于LBM的局部应用评估单元界面处的通量。界面通量仅通过分布函数计算。但是，涉及太多分发功能的代码实现仍然不够简单。并且分布函数的计算仍将花费相对较大的计算资源。我们注意到，分布函数的某些时刻可以直接简化为宏观变量。因此，为了进一步简化代码实现并提高MLBFS的计算效率，我们提出了一种简化的MLBFS，它结合了分布函数和宏观变量来重构通量。自然，我们可以期望简化的方法可以提高计算效率，同时保持原始MLBFS的数值准确性和可靠性。进行了拉普拉斯定律，瑞利-泰勒不稳定性，浮力下的气泡上升以及液滴在液膜上飞溅的数值实验，以评估简化的MLBFS。结果表明，我们的方法最多可以节省为了进一步简化代码实现并提高MLBFS的计算效率，我们提出了一种简化的MLBFS，它结合了分布函数和宏观变量来重构通量。自然，我们可以期望简化的方法可以提高计算效率，同时保持原始MLBFS的数值准确性和可靠性。进行了拉普拉斯定律，瑞利-泰勒不稳定性，浮力下的气泡上升以及液滴在液膜上飞溅的数值实验，以评估简化的MLBFS。结果表明，我们的方法最多可以节省为了进一步简化代码实现并提高MLBFS的计算效率，我们提出了一种简化的MLBFS，它结合了分布函数和宏观变量来重构通量。自然，我们可以期望简化的方法可以提高计算效率，同时保持原始MLBFS的数值准确性和可靠性。进行了拉普拉斯定律，瑞利-泰勒不稳定性，浮力下的气泡上升以及液滴在液膜上飞溅的数值实验，以评估简化的MLBFS。结果表明，我们的方法最多可以节省自然，我们可以期望简化的方法可以提高计算效率，同时保持原始MLBFS的数值准确性和可靠性。进行了拉普拉斯定律，瑞利-泰勒不稳定性，浮力下的气泡上升以及液滴在液膜上飞溅的数值实验，以评估简化的MLBFS。结果表明，我们的方法最多可以节省自然，我们可以期望简化的方法可以提高计算效率，同时保持原始MLBFS的数值准确性和可靠性。进行了拉普拉斯定律，瑞利-泰勒不稳定性，浮力下的气泡上升以及液滴在液膜上飞溅的数值实验，以评估简化的MLBFS。结果表明，我们的方法最多可以节省原始计算时间的18.32 ％。简化的方法优于原始方法，特别是对于具有大量网格的情况。

更新日期：2021-01-15

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