A high-precision discrete scheme for Forchheimer flow based on the finite analytic method

This study proposes a finite analytic method (FAM) for simulating Forchheimer flow in heterogeneous porous media, extending the established FAM framework originally developed for Darcy flow. Conventional numerical methods exhibit deteriorating accuracy under strong heterogeneity due to systematic underestimation of nodal transmissibility. The proposed FAM resolves this limitation by reconstructing the transmissibility tensor through local analytical solutions, ensuring accuracy independent of heterogeneity intensity. Compared with harmonic averaging techniques, this approach demonstrates superior precision in strongly heterogeneous systems. The method achieves subgrid resolution through localized subgrid refinement while maintaining computational practicality, requiring only modest grid adjustments to capture complex flow patterns in extreme heterogeneity scenarios.