The weak Galerkin method for the miscible displacement of incompressible fluids in porous media on polygonal mesh

In this paper, we develop a robust weak Galerkin discretization for the incompressible miscible displacement problem in porous media, which is a nonlinear time-dependent system. The scheme we constructed is positive definite and flexible by arbitrarily shaped polygonal mesh without imposing extra co...

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Bibliographic Details
Published in:Applied numerical mathematics 2023-03, Vol.185, p.530-548
Main Authors: Zhao, Jijing, Gao, Fuzheng, Rui, Hongxing
Format: Article
Language:English
Subjects:
Backward difference
Error estimates
Finite element methods
Incompressible miscible displacement
Weak Galerkin methods
Citations: Items that this one cites
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Summary:In this paper, we develop a robust weak Galerkin discretization for the incompressible miscible displacement problem in porous media, which is a nonlinear time-dependent system. The scheme we constructed is positive definite and flexible by arbitrarily shaped polygonal mesh without imposing extra conditions on the stabilization. The other feature of our method is that there is no limitation on the ratio of time-step and spatial mesh size. Error estimates are derived for concentration and pressure in the L2 norm and energy norm, respectively. Extensive numerical experiments, including realistic test cases, have been conducted to verify our theoretical results and the efficiency of the method.
ISSN:0168-9274
1873-5460
DOI:10.1016/j.apnum.2022.12.012