In porous media, limitations imposed by macroscale laws can be avoided with a dual-scale model, in which the pore-scale phenomena of interest are modelled directly over a large number of realisations. Such a model requires a robust, accurate and efficient pore-scale solver. We compare the boundary element method (BEM) and two variants of the lattice Boltzmann method (LBM) as pore-scale solvers of 2D incompressible flow. The methods are run on a number of test cases and the performance of each simulation is assessed according to the mean velocity error and the computational runtime. Both the porous geometry (porosity, shape and complexity), and the Reynolds number (from Stokes to visco-inertial flow) are varied between the test cases. We find that, for Stokes flow, BEM provides the most efficient and accurate solution in simple geometries (with small boundary length) or when a large runtime is practical. In all other situations we consider, one of the variants of LBM performs best. We furthermore demonstrate that these findings also apply in a dual-scale model of Stokes flow through a locally-periodic medium.

在多孔介质中，可以通过双尺度模型来避免宏观尺度定律带来的限制，其中感兴趣的孔隙尺度现象是直接在大量实现上建模的。这样的模型需要一个稳健、准确且高效的孔隙尺度求解器。我们比较了边界元法 (BEM) 和格子玻尔兹曼法 (LBM) 的两种变体作为二维不可压缩流的孔隙尺度求解器。这些方法在许多测试用例上运行，并根据平均速度误差和计算运行时间评估每个模拟的性能。测试用例之间的多孔几何形状（孔隙率、形状和复杂性）和雷诺数（从斯托克斯到粘惯性流）都不同。我们发现，对于斯托克斯流，边界元法在简单几何形状（边界长度较小）或实际运行时间较长时提供了最有效和最准确的解决方案。在我们考虑的所有其他情况下，LBM 的一种变体表现最好。我们进一步证明，这些发现也适用于通过局部周期性介质的斯托克斯流的双尺度模型。