An FFT‐based Galerkin method for the effective permeability of porous material

Abstract

AbstractA numerical scheme which is a combination of FFT and Galerkin methods is proposed for calculating the effective permeability of periodic porous material. First, a periodic stress field whose divergence is equal to the subtraction of body force from prescribed pressure gradient is introduced to reformulate the governing equations. Then, an auxiliary problem is established to replace the prescribed pressure gradient with the resulting initial prescribed stress. An FFT‐based Galerkin method of stress control type, the associated projection operator for zero divergence condition and the treatment of composite pixels/voxels are presented for solving the viscous flow in periodic porous material. Finally, numerical examples of viscous flows in 2D parallel fissured medium, 2D medium with regularly packed squares, 2D medium with regularly packed and rotated squares, 3D medium with regularly packed ellipsoids, and 3D medium with randomly packed ellipsoids are implemented. Numerical results calculated by FFT‐based Galerkin method agree well with analytical solutions and finite element results. The proposed FFT‐based Galerkin method is effective for predicting the macro permeability of porous material with complex meso structures.