Year: 2020
Author: Weiwei Sun, Chengda Wu
International Journal of Numerical Analysis and Modeling, Vol. 17 (2020), Iss. 3 : pp. 350–367
Abstract
The paper focuses on numerical study of the incompressible miscible flow in porous media. The proposed algorithm is based on a fully decoupled and linearized scheme in the temporal direction, classical Galerkin-mixed approximations in the FE space ($V^r_h$, $S^{r-1}_h$ × $H^{r-1}_h$) ($r$ ≥ 1) in the spatial direction and a post-processing technique for the velocity/pressure, where $V^r_h$ and $S^{r-1}_h$ × $H^{r-1}_h$ denotes the standard $C^0$ Lagrange FE and the Raviart-Thomas FE spaces, respectively. The decoupled and linearized Galerkin-mixed FEM enjoys many advantages over existing methods. At each time step, the method only requires solving two linear systems for the concentration and velocity/pressure. Analysis in our recent work [37] shows that the classical Galerkin-mixed method provides the optimal accuracy $O$($h^{r+1}$) for the numerical concentration in $L^2$-norm, instead of $O$($h^r$) as shown in previous analysis. A new numerical velocity/pressure of the same order accuracy as the concentration can be obtained by the post-processing in the proposed algorithm. Extensive numerical experiments in both two- and three-dimensional spaces, including smooth and non-smooth problems, are presented to illustrate the accuracy and stability of the algorithm. Our numerical results show that the one-order lower approximation to the velocity/pressure does not influence the accuracy of the numerical concentration, which is more important in applications.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2020-IJNAM-16863
International Journal of Numerical Analysis and Modeling, Vol. 17 (2020), Iss. 3 : pp. 350–367
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Galerkin-mixed FEM incompressible miscible flow in porous media fully linearized scheme.