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Volume 37, Issue 3
Mortar Finite Element Method for the Coupling of Time Dependent Navier-Stokes and Darcy Equations

Xin Zhao & Chuanjun Chen

DOI: 10.4208/cicp.OA-2023-0009

Commun. Comput. Phys., 37 (2025), pp. 701-739.

Published online: 2025-03

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  • 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.

  • Keywords

Darcy equations, Navier-Stokes equations, coupling, finite elements, mortar.

  • AMS Subject Headings

76D05, 76S05, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-37-701, author = {Zhao , Xin and Chen , Chuanjun}, title = {Mortar Finite Element Method for the Coupling of Time Dependent Navier-Stokes and Darcy Equations}, journal = {Communications in Computational Physics}, year = {2025}, volume = {37}, number = {3}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2023-0009}, url = {http://global-sci.org/intro/article_detail/cicp/23919.html} }
TY - JOUR T1 - Mortar Finite Element Method for the Coupling of Time Dependent Navier-Stokes and Darcy Equations AU - Zhao , Xin AU - Chen , Chuanjun JO - Communications in Computational Physics VL - 3 SP - 701 EP - 739 PY - 2025 DA - 2025/03 SN - 37 DO - http://doi.org/10.4208/cicp.OA-2023-0009 UR - https://global-sci.org/intro/article_detail/cicp/23919.html KW - Darcy equations, Navier-Stokes equations, coupling, finite elements, mortar. AB -

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.

Zhao , Xin and Chen , Chuanjun. (2025). Mortar Finite Element Method for the Coupling of Time Dependent Navier-Stokes and Darcy Equations. Communications in Computational Physics. 37 (3). 701-739. doi:10.4208/cicp.OA-2023-0009
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