Generalized multiscale approximation of a multipoint flux mixed finite element method for Darcy–Forchheimer model

In this paper, we propose a multiscale method for the Darcy–Forchheimer model in highly heterogeneous porous media. The problem is solved framework of generalized finite element (GMsFEM) combined with multipoint flux mixed (MFMFE) method. We consider MFMFE that utilizes lowest order Brezzi–Douglas–Marini ( BDM 1 ) spaces approximation velocity and pressure. symmetric trapezoidal quadrature rule employed integral bilinear forms related to variables so local elimination allowed which leads cell-centered system construct space pressure solve on coarse grid following GMsFEM framework. offline stage, snapshot perform spectral decompositions get smaller dimension. online use Newton iterative algorithm nonlinear obtain solution, reduces number iterations greatly compared standard Picard algorithm. Based basis functions calculate each enrich iteratively. contain important global information are effective reduce relative errors substantially. Numerical examples provided highlight performance proposed