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Abstract <p>This research presents a mixed generalized multiscale finite element method (mixed GMsFEM) algorithm for the Darcy–Forchheimer–Brinkman model in heterogeneous media. This model governs nonlinear Darcy flow with significant inertial effects at high flow velocities. The fine-grid approximation utilizes a mixed finite element method (FEM), with nonlinearity resolved via Picard iteration. The proposed model reduction approach, mixed GMsFEM, employs local spectral decomposition to construct multiscale basis functions within each local domain using a snapshot space. These basis functions effectively capture the influence of high-contrast coefficients. Numerical results for a two-dimensional heterogeneous domain demonstrate the method’s high accuracy for nonlinear problems. The investigation reveals that accuracy is weakly dependent on the magnitude of the nonlinearity.</p>

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Multiscale Modeling for Darcy–Forchheimer–Brinkman Model

  • 期刊论文

  • 发表日期：

    2026年1月1日

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  • D. A. Spiridonov

摘要

Abstract

This research presents a mixed generalized multiscale finite element method (mixed GMsFEM) algorithm for the Darcy–Forchheimer–Brinkman model in heterogeneous media. This model governs nonlinear Darcy flow with significant inertial effects at high flow velocities. The fine-grid approximation utilizes a mixed finite element method (FEM), with nonlinearity resolved via Picard iteration. The proposed model reduction approach, mixed GMsFEM, employs local spectral decomposition to construct multiscale basis functions within each local domain using a snapshot space. These basis functions effectively capture the influence of high-contrast coefficients. Numerical results for a two-dimensional heterogeneous domain demonstrate the method’s high accuracy for nonlinear problems. The investigation reveals that accuracy is weakly dependent on the magnitude of the nonlinearity.