In this work, we improve the traditional adaptive mesh refinement (AMR) by combining it with the finite analytical method (FAM) to solve the multiphase flow in heterogeneous porous media numerically. The FAM can provide rather accurate internodal transmissibility, and it is employed to improve the accuracy of coarsening and refining processes in AMR. The high performance of the proposed AMR‐FAM is indicated through numerical tests for solving the two‐phase flow in 2D heterogeneous media. The numerical simulation results indicate that the proposed AMR‐FAM is more accurate than the traditional AMR‐FAM. Compared with the simulation in the original fine grids, the proposed AMR‐FAM can provide nearly the same results. Moreover, the computational cost in the AMR grids is only approximately one‐third of the cost in the original fine grids according to our numerical tests.

中文翻译：

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基于有限解析方法的异质多孔介质二维流动自适应网格细化


在这项工作中，我们通过将传统的自适应网格细化 （AMR） 与有限解析方法 （FAM） 相结合，以数值方式求解非均相多孔介质中的多相流，从而对其进行了改进。FAM 可以提供相当准确的结节间传递率，并用于提高 AMR 中粗化和细化过程的准确性。通过用于解决 2D 非均质介质中两相流的数值测试来证明所提出的 AMR-FAM 的高性能。数值模拟结果表明，所提出的 AMR-FAM 比传统的 AMR-FAM 更准确。与原始精细网格中的模拟相比，所提出的 AMR-FAM 可以提供几乎相同的结果。此外，根据我们的数值测试，AMR 网格的计算成本仅为原始精细网格成本的三分之一左右。