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Finite analytic method for 2D steady fluid flows in heterogeneous porous media with unstructured grids
Author(s) -
Wang GuanWen,
Liu ZhiFeng,
Wang XiaoHong
Publication year - 2017
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5633
Subject(s) - porous medium , grid , flow (mathematics) , unstructured grid , computer science , permeability (electromagnetism) , mathematics , mathematical optimization , topology (electrical circuits) , geometry , porosity , materials science , combinatorics , membrane , biology , composite material , genetics
The finite analytic method (FAM) is developed to solve the 2D 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, 3 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.