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A novel median dual finite volume lattice Boltzmann method for incompressible flows on unstructured grids
International Journal of Modern Physics C ( IF 1.9 ) Pub Date : 2020-08-29 , DOI: 10.1142/s0129183120501739
Lei Xu 1, 2 , Wu Zhang 3 , Zhengzheng Yan 1, 2 , Zheng Du 4 , Rongliang Chen 1, 2
Affiliation  

A novel median dual finite volume lattice Boltzmann method (FV-LBM) for the accurate simulation of incompressible flows on unstructured grids is presented in this paper. The finite volume method is adopted to discretize the discrete velocity Boltzmann equation (DVBE) on median dual control volumes (CVs). In the previous studies on median dual FV-LBMs, the fluxes for each partial face have to be computed separately. In the present second-order scheme, we assume the particle distribution functions (PDFs) to be constant for all faces grouped around a particular edge. The fluxes are then evaluated using the low-diffusion Roe scheme at the midpoint of the edge, and the PDFs at the faces of the CV are obtained through piecewise linear reconstruction of the left and right states. The gradients of the PDFs are computed with the Green–Gauss approach. The presented scheme is validated on four benchmark flows: (a) pressure driven Poiseuille flow; (b) the backward-facing step flow with [Formula: see text], 100, 200 and 300; (c) the lid-driven flow with [Formula: see text] and 1000; and (d) the steady viscous flow past a circular cylinder with [Formula: see text], 20 and 40.

中文翻译:

一种用于非结构化网格上不可压缩流动的中值对偶有限体积格子 Boltzmann 方法

本文提出了一种新的中值对偶有限体积格子玻尔兹曼方法(FV-LBM),用于精确模拟非结构化网格上的不可压缩流动。采用有限体积法对中值对偶控制体积(CVs)上的离散速度玻尔兹曼方程(DVBE)进行离散化。在先前关于中值双 FV-LBM 的研究中,必须分别计算每个部分面的通量。在目前的二阶方案中,我们假设粒子分布函数 (PDF) 对于围绕特定边缘分组的所有面是恒定的。然后使用边缘中点的低扩散 Roe 方案评估通量,并通过左右状态的分段线性重建获得 CV 面的 PDF。PDF 的梯度是使用 Green-Gauss 方法计算的。所提出的方案在四个基准流上进行了验证:(a)压力驱动的泊肃叶流;(b) [公式:见正文]、100、200 和 300 的后向步骤流程;(c) [公式:见正文] 和 1000 的盖子驱动流动;(d) 用 [公式:见正文]、20 和 40 的圆柱体的稳定粘性流。
更新日期:2020-08-29
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