Finite analytic method for 2D steady fluid flows in heterogeneous porous media with unstructured grids

The finite analytic method is developed to solve the two-dimensional steady fluid flows in heterogeneous porous media with full tensor permeability on unstructured grids. The proposed FAM is constructed based upon the power-law analytic nodal solution in the angular domain with arbitrary shape. When approaching the grid node joining the subdomains, three different flow patterns may exist: power-law flow, linear flow or the stagnant flow. Based on the nodal analytic solution, the triangle-based FAM is proposed. Numerical examples show that the proposed numerical scheme makes the convergences much quickly than the traditional methods, typically the weighted harmonic mean method under the cell refinement. In practical applications, the grid refinement parameter n=2 or n=3 is recommended, and the relative error of the calculated equivalent permeability will below 4% independent of the heterogeneity. In contrast, when using the traditional numerical scheme the refinement ratio for the grid cell needs to increase dramatically to get an accurate result, especially for strong heterogeneous porous medium.