Shale gas flow at the pore scale is very challenging to simulate due to high Knudsen numbers ($Kn$), low speeds and complicated pore geometries. The direct simulation BGK (DSBGK) method and the discrete velocity method (DVM) are promising methods to simulate three-dimensional (3D) gas flows in the shale rock. As the grid-convergence accuracy and computational cost highly depend on the spatial and molecular velocity grids, here we present a rigorous study of the computational performance of the two methods by simulating gas flows through the standard 3D Sierpinski carpet. In this study, we found reasonable agreement between the DSBGK and DVM simulations when comparing the velocity profiles and permeability curves obtained by using fine spatial and velocity grids. However, the grid convergence of the DSBGK simulation is faster than that of the DVM, which requires a very large number of spatial and velocity grids for convergence. Consequently, the DSBGK simulation is orders of magnitude cheaper than the DVM simulation in terms of the CPU time and memory usage. While the DVM requires a high-performance computing facility to meet the memory demand of several hundreds of gigabyte for simulating this 3D flow problem, the DSBGK simulation can run on an ordinary laptop. This work therefore demonstrates the DSBGK method as a practical simulation tool for 3D pore-scale gas flows in the shale rock. Converged results generated in this study can be used as comparison data by other simulation methods.

由于高克努森数（$钾n$)、低速和复杂的孔隙几何形状。直接模拟 BGK (DSBGK) 方法和离散速度方法 (DVM) 是模拟页岩中三维 (3D) 气流的有前途的方法。由于网格收敛的准确性和计算成本高度依赖于空间和分子速度网格，因此在此我们通过模拟通过标准3D Sierpinski地毯的气流来对这两种方法的计算性能进行严格的研究。在这项研究中，当比较使用精细空间和速度网格获得的速度剖面和渗透率曲线时，我们发现 DSBGK 和 DVM 模拟之间存在合理的一致性。然而，DSBGK 模拟的网格收敛速度比 DVM 快，这需要非常大量的空间和速度网格进行收敛。最后，DSBGK 模拟在 CPU 时间和内存使用方面比 DVM 模拟便宜几个数量级。虽然 DVM 需要高性能计算设施来满足数百 GB 的内存需求来模拟这个 3D 流问题，但 DSBGK 模拟可以在普通笔记本电脑上运行。因此，这项工作证明 DSBGK 方法是页岩中 3D 孔隙尺度气流的实用模拟工具。本研究中产生的收敛结果可以作为其他模拟方法的比较数据。DSBGK 模拟可以在普通笔记本电脑上运行。因此，这项工作证明 DSBGK 方法是页岩中 3D 孔隙尺度气流的实用模拟工具。本研究中产生的收敛结果可以作为其他模拟方法的比较数据。DSBGK 模拟可以在普通笔记本电脑上运行。因此，这项工作证明 DSBGK 方法是页岩中 3D 孔隙尺度气流的实用模拟工具。本研究中产生的收敛结果可以作为其他模拟方法的比较数据。