Mortar Finite Element Method for the Coupling of Time Dependent Navier-Stokes and Darcy Equations
Year: 2025
Author: Xin Zhao, Chuanjun Chen
Communications in Computational Physics, Vol. 37 (2025), Iss. 3 : pp. 701–739
Abstract
The article discusses a nonlinear system that is dependent on time and coupled by incompressible fluid and porous media flow. Treating Darcy flow as dual-mixed form, we propose a variational formulation and prove the well-posedness of weak solutions. The discretization of domain is accomplished using a triangular mesh, with the lowest order Raviart-Thomas element utilized for Darcy equations and Bernardi-Raugel element used for Navier-Stokes equations. Using the mortar method, we construct the spaces from which numerical solutions are sought. Based on backward Euler method, we establish a fully discrete algorithm. At each single time level, the first-order convergence is demonstrated through the use of the Gronwall inequality. Numerical experiments are provided to illustrate the algorithm’s effectiveness in approximating solutions.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2023-0009
Communications in Computational Physics, Vol. 37 (2025), Iss. 3 : pp. 701–739
Published online: 2025-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 39
Keywords: Darcy equations Navier-Stokes equations coupling finite elements mortar.
Author Details
Xin Zhao Email
Chuanjun Chen Email