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Numerics of the lattice boltzmann method on nonuniform grids: Standard LBM and finite-difference LBM

机译:非均匀网格上的格子Boltzmann方法的数值:标准LBM和有限差分LBM

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The present study is focused on the comparison between the standard "collide-and-stream" lattice Boltzmann method (LBM) and the Lax-Wendroff-based finite-difference LBM (FDLBM) on block-structured nonuniform grids with an adaptive mesh refinement (AMR) strategy. While the standard LBM (SLBM) is found to be slightly faster than the FDLBM, the latter is shown to be more stable at higher Reynolds numbers. Although both approaches are as accurate in simulation of fluid flow problems, the SLBM has a more complicated algorithm and its implementation is more involved; this is mainly because, in applying SLBM, the AMR blocks at different refinement levels do not advance in time simultaneously. On the other hand, the underlying differences between the cell-center and cell-vertex data structures are explained and their advantages and disadvantages are highlighted. In general, the cell-center data structure is favorable because it is more efficient in terms of computational time and memory. The effect of the interpolation schemes on the order of accuracy of the LBM is also investigated. It is reestablished that the popular linear interpolation degrades the order of accuracy of LBM to first order. A variety of benchmark studies, including Taylor-Green decaying vortex, gravity-driven Poiseuille flow, thin shear layer instability, and unsteady flow past a square cylinder, are carried out to assess SLMB and FDLBM with a multiple-relaxation-time collision operator. (C) 2014 Elsevier Ltd. All rights reserved.
机译:本研究的重点是在具有自适应网格细化的块结构非均匀网格上,比较标准的“碰撞流”晶格玻尔兹曼方法(LBM)和基于Lax-Wendroff的有限差分LBM(FDLBM)。 AMR)策略。虽然发现标准LBM(SLBM)比FDLBM快一点,但事实证明后者在更高的雷诺数下更稳定。尽管这两种方法在模拟流体流动问题上都一样准确,但是SLBM具有更复杂的算法,并且涉及更多的实现。这主要是因为在应用SLBM时,不同细化级别的AMR块不会同时提前。另一方面,解释了单元中心和单元顶点数据结构之间的潜在差异,并突出了它们的优缺点。通常,单元中心数据结构是有利的,因为它在计算时间和存储方面更有效。还研究了插值方案对LBM精度的影响。重新确定的是,流行的线性插值法将LBM的精度从一级降到了一级。为了进行SLMB和FDLBM的多重弛豫时间碰撞算子评估,进行了各种基准研究,包括泰勒-格林衰变涡旋,重力驱动的泊肃叶流,薄剪切层不稳定性和经过方形圆柱体的非稳态流。 (C)2014 Elsevier Ltd.保留所有权利。

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