<abstract xmlns="http://www.w3.org/1999/xhtml"><p>We present a general finite volume method to solve a coupled Stokes-Darcy problem, we propose two domains corresponding to fluid region and porous region with a physical intersection. At the contact interface between the fluid region and the porous media we impose two conditions; the first one is the normal continuity of the velocity and the second one is the continuity of the pressure. Furthermore, due to the lack of information about both the velocity and the pressure on the interface, we will use Schwarz domain decomposition. In Darcy equations, the tensor of permeability will be considered as variable, since it depends on both the properties of the porous medium and the viscosity of the fluid. Numerical examples are presented to demonstrate the efficiency of the proposed method.</p></abstract>

We present a general finite volume method to solve a coupled Stokes-Darcy problem, we propose two domains corresponding to fluid region and porous region with a physical intersection. At the contact interface between the fluid region and the porous media we impose two conditions; the first one is the normal continuity of the velocity and the second one is the continuity of the pressure. Furthermore, due to the lack of information about both the velocity and the pressure on the interface, we will use Schwarz domain decomposition. In Darcy equations, the tensor of permeability will be considered as variable, since it depends on both the properties of the porous medium and the viscosity of the fluid. Numerical examples are presented to demonstrate the efficiency of the proposed method.

A Discrete Duality Finite Volume Method for Coupling Darcy and Stokes Equations

Moroccan Journal of Pure and Applied Analysis

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"A Discrete Duality Finite Volume Method for Coupling Darcy and Stokes Equations"}

We present a general finite volume method to solve a coupled Stokes-Darcy problem, we propose two domains corresponding to fluid region and porous region with...

A Discrete Duality Finite Volume Method for Coupling Darcy and Stokes Equations

Published Online: Nov 08, 2019

Page range: 46 - 62

Received: May 08, 2019

Accepted: Aug 19, 2019

DOI: https://doi.org/10.2478/mjpaa-2019-0005

Keywords
Stokes, Darcy, Coupled Problem, Finite Volume Method, Schwarz, Domain Decomposition Method

© 2019 M. Rhoudaf et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

A Discrete Duality Finite Volume Method for Coupling Darcy and Stokes Equations

Published Online: Nov 08, 2019

Page range: 46 - 62

Received: May 08, 2019

Accepted: Aug 19, 2019

DOI: https://doi.org/10.2478/mjpaa-2019-0005

KeywordsStokes, Darcy, Coupled Problem, Finite Volume Method, Schwarz, Domain Decomposition Method

© 2019 M. Rhoudaf et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Stokes, Darcy, Coupled Problem, Finite Volume Method, Schwarz, Domain Decomposition Method