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A Robin-Robin Domain Decomposition Method for a Stokes-Darcy Structure Interaction with a Locally Modified Mesh

Published online by Cambridge University Press:  09 August 2018

Zhaohui Wang ,
Zhilin Li  and
Sharon Lubkin
Zhaohui Wang*
Affiliation:
Department of Mathematics and Center for Research in Scientific Computation (CRSC), North Carolina State University, Raleigh, NC 27695, USA.
Zhilin Li*
Affiliation:
Department of Mathematics and Center for Research in Scientific Computation (CRSC), North Carolina State University, Raleigh, NC 27695, USA.
Sharon Lubkin*
Affiliation:
Department of Mathematics and Center for Research in Scientific Computation (CRSC), North Carolina State University, Raleigh, NC 27695, USA.
*
Email address: zwang24@ncsu.edu
Email: zhilin@ncsu.edu
*Corresponding author.Email: lubkin@ncsu.edu
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Abstract

A new numerical method based on locally modified Cartesian meshes is proposed for solving a coupled system of a fluid flow and a porous media flow. The fluid flow is modeled by the Stokes equations while the porous media flow is modeled by Darcy's law. The method is based on a Robin-Robin domain decomposition method with a Cartesian mesh with local modifications near the interface. Some computational examples are presented and discussed.

Keywords

65N3065N5065N5576D0776S05Stokes-Darcy fluid structure interactionsRobin-Robin domain decomposition methodbody fitted meshlocally modified meshBJS interface condition
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 7 , Issue 4 , November 2014 , pp. 435 - 446
Copyright
Copyright © Global Science Press Limited 2014

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References

[1] Börgers, C.. A triangulation algorithm for fast elliptic solvers based on domain imbedding. SIAM J. Numer. Anal., 27:1187–1196, 1990.Google Scholar
[2] Beavers, G. and Joseph, D.. Boundary conditions at a naturally permeable wall. J. Fluid Mech., 30:197–207, 1967.Google Scholar
[3] Cao, Y., Gunzburger, M., He, X., and Wang, X.. Robin-Robin domain decomposition methods for the steady-state Stokes-Darcy system with the Beavers-Joseph interface condition. Numer. Math., 117:601–629, 2011.Google Scholar
[4] Chen, W., Gunzburger, M., Hua, F., and Wang, X.. A parallel Robin-Robin domain decomposition method for the Stokes-Darcy system. SIAM J. Numer. Anal., 49(3):1064–1084, 2011.Google Scholar
[5] Discacciati, M. and Quarteroni, A.. Convergence analysis of a subdomain iterative method for the finite element approximation of the coupling of Stokes and Darcy equations. Com-put. Vis. Sci., 6(2-3):93–103, 2004.Google Scholar
[6] Discacciati, M., Quarteroni, A., and Valli, A.. Robin-Robin domain decomposition methods for the Stokes-Darcy coupling. SIAM J. Numer. Anal., 45(3):1246–1268, 2007.Google Scholar
[7] Gong, Y., Li, B., and Li, Z.. Immersed-interface finite-element methods for elliptic interface problems with non-homogeneous jump conditions. SIAM J. Numer. Anal., 46:472–495, 2008.Google Scholar
[8] Jäger, W. and Mikelić, A.. On the interface boundary condition of Beavers, Joseph, and Saffman. SIAM J. Appl. Math., 60(4):1111–1127, 2000.Google Scholar
[9] Jones, I.. Low Reynolds number flow past a porous spherical shell. Proc. Camb. Phil. Soc., 73:231–238, 1973.Google Scholar
[10] Layton, W.J., Schieweck, F., and Yotov, I.. Coupling fluid flow with porous media flow. SIAM J. Numer. Anal., 40(6):2195–2218, 2002.Google Scholar
[11] Li, Z., Lin, T., and Wu, X.. New Cartesian grid methods for interface problem using finite element formulation. Numer. Math., 96:61–98, 2003.Google Scholar
[12] Li, Z. and Song, P.. An adaptive mesh refinement strategy for immersed boundary/interface methods. Commun Comput Phys., 12(2):515–527, 2012.Google Scholar
[13] Li, Z. and Song, P.. Adaptive mesh refinement techniques for the immersed interface method applied to flow problems. Computers and Structures, 122:249–258, 2013.CrossRefGoogle ScholarPubMed
[14] Saffman, P.. On the boundary condition at the interface of a porous medium. Stud. Appl. Math., 1:77–84, 1971.Google Scholar
[15] Xie, H., Ito, K., Li, Z., and Toivanen, J.. A finite element method for interface problems with locally modified triangulation. Contemporary Mathematics, 466:179–190, 2008.Google Scholar