JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (10): 38-47.doi: 10.6040/j.issn.1671-9352.9.2021.007

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Two-grid mixed finite element method for incompressible Darcy-Forchheimer miscible displacement problems

RUI Hong-xing, LONG Xin-yu   

  1. School of Mathematics, Shandong University, Jinan 250100, Shandong, China
  • Published:2021-09-28

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Abstract: In this paper, a two-grid mixed finite element method is used to solve the incompressible miscible displacement problem in porous media, in which the relationship between velocity and pressure conforms to Darcy-Forchheimer law. The purpose of the method is to transform the solving of a large nonlinear system on the fine grid into the solving of a small nonlinear system on the coarse-grid and the solving of a linear system on the fine-grid. The iterative method is needed to solve the nonlinear system. After this transformation only the linear system need to be solved on fine-grid, which can greatly improve the speed of calculation. In the paper, we use piecewise constant element to approximate the velocity and use piecewise continuous linear element to approximate the pressure and concentration. Numerical experiments are carried out to show the error on the fine grid and computational efficiency.

Key words: mixed finite element, two-grid method, Darcy-Forchheimer flow, miscible displacement

CLC Number: 

  • O241
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