Abstract Lattice Boltzmann method (LBM) is widely adopted in simulating flow and reactive transport in porous media due to its easy treatment of boundaries and high computational efficiency. There have been various boundary schemes developed in the LBM due to their vital roles when dealing with fluid-solid interface. In the present work, we aim to review and intercompare all the single-node boundary schemes (including the existing schemes and our newly-developed schemes) in the LBM through a series of numerical experiments from simple benchmarking cases to realistic applications. Both the accuracy and computational efficiency of all the schemes are evaluated and analyzed. Among the existing schemes, it is known that the bounce-back scheme (BB) is commonly employed at the boundaries in the LBM. However, the BB is of only first-order spatial accuracy when zero-velocity is not exactly located in the middle of the fluid and solid nodes, which cannot be guaranteed in porous media flows due to the complex pore structures. Therefore, fine grids are usually generated to obtain satisfactory results yet computationally expensive. Recently, a second-order single-node boundary scheme (SSN), which is more flexible than the BB while retaining the locality, has been proposed (Zhao et al, J. Comput. Phys., 329:1-15, 2017 Zhao and Yong (2017)). Unfortunately, the SSN fails to provide a viscosity-independent permeability, i.e., the predicted permeability is related to the fluid viscosity, which is unphysical. Based on the SSN, we first developed a magic second-order single-node boundary scheme (MSSN) to overcome this shortcoming based on the Chapman-Enskog analysis of the two-relaxation-time lattice Boltzmann equation (TRT-LBE) model. Comparative study of the BB, SSN/MSSN, and another single-node boundary scheme, i.e., the improved bounce-back scheme (IBB)/the magic improved bounce-back scheme (MIBB) is then performed both theoretically and numerically. Numerical simulations of porous media flows in both two and three dimensions confirm that the BB, MIBB, and MSSN can obtain the viscosity-independent permeability, while the IBB and SSN fail to do so. First of all, as benchmarking tests, flow through a 2D fracture is studied using different schemes, the results of which show that the IBB and SSN cannot provide viscosity-independent permeability while such drawbacks can be overcome by the BB/MIBB/MSSN. Furthermore, simulations of flows through a hexagonal array of cylinders and a 3D sphere packing demonstrate that the MSSN is more accurate than both the BB and MIBB. Finally, for porous media samples generated from the micro-CT images where the locations of the boundaries are not exactly known, the MSSN is more flexible to locate the positions of the fluid-solid interface than the BB and MIBB, which in turn can provide more accurate descriptions of the fluid flow. The current intercomparison study will benefit the community by providing comprehensive review and evaluation of the performance when using different single-node boundary schemes in the LBM.

中文翻译：

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使用格子 Boltzmann 方法模拟多孔介质中的流动：从基准测试到应用的单节点边界方案的比较

摘要 格子Boltzmann方法(LBM)因其边界易于处理和计算效率高而被广泛用于模拟多孔介质中的流动和反应输运。由于 LBM 在处理流固界面时的重要作用，已经在 LBM 中开发了各种边界方案。在目前的工作中，我们的目标是通过从简单的基准案例到实际应用的一系列数值实验来回顾和比较 LBM 中的所有单节点边界方案（包括现有方案和我们新开发的方案）。对所有方案的准确性和计算效率进行了评估和分析。在现有的方案中，众所周知，反弹方案（BB）通常用于LBM的边界处。然而，当零速度不完全位于流体和固体节点的中间时，BB 仅具有一阶空间精度，由于复杂的孔隙结构，这在多孔介质流动中无法保证。因此，通常生成精细网格以获得令人满意的结果，但计算成本很高。最近，提出了一种二阶单节点边界方案（SSN），它在保留局部性的同时比 BB 更灵活（Zhao et al, J. Comput. Phys., 329:1-15, 2017 Zhao和 Yong (2017))。不幸的是，SSN 无法提供与粘度无关的渗透率，即预测渗透率与流体粘度有关，这是非物理的。根据 SSN，我们首先开发了一种神奇的二阶单节点边界方案 (MSSN) 来克服这个缺点，基于对双松弛时间格子玻尔兹曼方程 (TRT-LBE) 模型的 Chapman-Enskog 分析。然后在理论上和数值上对 BB、SSN/MSSN 和另一种单节点边界方案，即改进的反弹方案 (IBB)/魔法改进的反弹方案 (MIBB) 进行比较研究。二维和三维多孔介质流动的数值模拟证实，BB、MIBB 和 MSSN 可以获得与粘度无关的渗透率，而 IBB 和 SSN 则不能这样做。首先，作为基准测试，使用不同的方案研究通过二维裂缝的流动，结果表明，IBB 和 SSN 不能提供与粘度无关的渗透率，而 BB/MIBB/MSSN 可以克服这些缺点。此外，通过六边形圆柱阵列和 3D 球体填充的流动模拟表明，MSSN 比 BB 和 MIBB 更准确。最后，对于从边界位置不准确的微 CT 图像生成的多孔介质样本，MSSN 比 BB 和 MIBB 更灵活地定位流固界面的位置，这反过来可以提供更准确地描述流体流动。当前的比对研究将通过对 LBM 中使用不同单节点边界方案时的性能进行全面审查和评估，从而使社区受益。通过六边形圆柱阵列和 3D 球体堆积的流动模拟表明，MSSN 比 BB 和 MIBB 更准确。最后，对于从边界位置不准确的微 CT 图像生成的多孔介质样本，MSSN 比 BB 和 MIBB 更灵活地定位流固界面的位置，这反过来可以提供更准确地描述流体流动。当前的比对研究将通过对 LBM 中使用不同单节点边界方案时的性能进行全面审查和评估，从而使社区受益。通过六边形圆柱阵列和 3D 球体堆积的流动模拟表明，MSSN 比 BB 和 MIBB 更准确。最后，对于从边界位置不准确的微 CT 图像生成的多孔介质样本，MSSN 比 BB 和 MIBB 更灵活地定位流固界面的位置，这反过来可以提供更准确地描述流体流动。当前的比对研究将通过对 LBM 中使用不同单节点边界方案时的性能进行全面审查和评估，从而使社区受益。对于边界位置不准确的微 CT 图像生成的多孔介质样品，MSSN 比 BB 和 MIBB 更灵活地定位流固界面的位置，从而可以提供更准确的流体流动的描述。当前的比对研究将通过对 LBM 中使用不同单节点边界方案时的性能进行全面审查和评估，从而使社区受益。对于边界位置未知的微 CT 图像生成的多孔介质样本，MSSN 比 BB 和 MIBB 更灵活地定位流固界面的位置，从而可以提供更准确的流体流动的描述。当前的比对研究将通过对 LBM 中使用不同单节点边界方案时的性能进行全面审查和评估，从而使社区受益。