Volume 12, Issue 5
An Upwind Mixed Finite Element Method on Changing Meshes for Positive Semi-Definite Oil-Water Displacement of Darcy-Forchheimer Flow in Porous Media

Yirang Yuan, Huailing Song, Changfeng Li & Tongjun Sun

Adv. Appl. Math. Mech., 12 (2020), pp. 1196-1223.

Published online: 2020-07

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  • Abstract

An upwind mixed finite element method is proposed on changing meshes for solving a positive semi-definite miscible displacement problem of Darcy-Forchheimer flow in three-dimensional porous media. The pressure and velocity could be obtained together by using a mixed finite element, and the computational accuracy of velocity is improved. The concentration equation is solved by the upwind mixed finite element scheme on changing meshes, where the upwind approximation and an expanded mixed finite element are adopted for the convection and diffusion, respectively. It solves the convection-dominated diffusion problem well and has the following improvements. First, the conservation of mass, an important physical nature, is preserved. Second, it has high order computational accuracy. An optimal-order error estimates is concluded. Numerical experiments illustrate the efficiency and application of the presented scheme.

  • Keywords

Darcy-Forchheimer flow, positive semi-definite problem, adaptive changing meshes, upwind mixed finite element method, convergence analysis.

  • AMS Subject Headings

65N30, 65N12, 65M15, 65M60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-12-1196, author = {Yirang Yuan , and Huailing Song , and Changfeng Li , and Tongjun Sun , }, title = {An Upwind Mixed Finite Element Method on Changing Meshes for Positive Semi-Definite Oil-Water Displacement of Darcy-Forchheimer Flow in Porous Media}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2020}, volume = {12}, number = {5}, pages = {1196--1223}, abstract = {

An upwind mixed finite element method is proposed on changing meshes for solving a positive semi-definite miscible displacement problem of Darcy-Forchheimer flow in three-dimensional porous media. The pressure and velocity could be obtained together by using a mixed finite element, and the computational accuracy of velocity is improved. The concentration equation is solved by the upwind mixed finite element scheme on changing meshes, where the upwind approximation and an expanded mixed finite element are adopted for the convection and diffusion, respectively. It solves the convection-dominated diffusion problem well and has the following improvements. First, the conservation of mass, an important physical nature, is preserved. Second, it has high order computational accuracy. An optimal-order error estimates is concluded. Numerical experiments illustrate the efficiency and application of the presented scheme.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2019-0256}, url = {http://global-sci.org/intro/article_detail/aamm/17745.html} }
TY - JOUR T1 - An Upwind Mixed Finite Element Method on Changing Meshes for Positive Semi-Definite Oil-Water Displacement of Darcy-Forchheimer Flow in Porous Media AU - Yirang Yuan , AU - Huailing Song , AU - Changfeng Li , AU - Tongjun Sun , JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 1196 EP - 1223 PY - 2020 DA - 2020/07 SN - 12 DO - http://doi.org/10.4208/aamm.OA-2019-0256 UR - https://global-sci.org/intro/article_detail/aamm/17745.html KW - Darcy-Forchheimer flow, positive semi-definite problem, adaptive changing meshes, upwind mixed finite element method, convergence analysis. AB -

An upwind mixed finite element method is proposed on changing meshes for solving a positive semi-definite miscible displacement problem of Darcy-Forchheimer flow in three-dimensional porous media. The pressure and velocity could be obtained together by using a mixed finite element, and the computational accuracy of velocity is improved. The concentration equation is solved by the upwind mixed finite element scheme on changing meshes, where the upwind approximation and an expanded mixed finite element are adopted for the convection and diffusion, respectively. It solves the convection-dominated diffusion problem well and has the following improvements. First, the conservation of mass, an important physical nature, is preserved. Second, it has high order computational accuracy. An optimal-order error estimates is concluded. Numerical experiments illustrate the efficiency and application of the presented scheme.

Yirang Yuan, Huailing Song, Changfeng Li & Tongjun Sun. (2020). An Upwind Mixed Finite Element Method on Changing Meshes for Positive Semi-Definite Oil-Water Displacement of Darcy-Forchheimer Flow in Porous Media. Advances in Applied Mathematics and Mechanics. 12 (5). 1196-1223. doi:10.4208/aamm.OA-2019-0256
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