多孔介质Darcy-Forchheimer不可压缩混溶驱动问题的二重网格混合元算法

doi:10.6040/j.issn.1671-9352.9.2021.007

摘要/Abstract

摘要： 研究采用二重网格混合有限元法求解多孔介质中不可压缩混相驱替问题,其中,该问题的速度与压力的关系由Darcy-Forchheimer定律描述。主要目的是将在细网格上求解一个大规模非线性系统转换为在粗网格上求解一个小规模非线性系统以及在细网格上求解一个线性系统。求解非线性系统需要用迭代法,而转换为线性系统后,只需要解线性代数方程组,可以大大提高运算的速度。在本文中,我们用混合元逼近速度和压力,用一般的有限元逼近组分浓度。在本文的数值实验中,我们验证了细网格上的误差估计,以及计算效率。

关键词: 混合元, 二重网格法, Darcy-Forchheimer, 混溶驱动

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

中图分类号:

O241

芮洪兴,龙新雨. 多孔介质Darcy-Forchheimer不可压缩混溶驱动问题的二重网格混合元算法[J]. 《山东大学学报(理学版)》, 2021, 56(10): 38-47.

RUI Hong-xing, LONG Xin-yu. Two-grid mixed finite element method for incompressible Darcy-Forchheimer miscible displacement problems[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(10): 38-47.

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