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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Parallel, non-iterative, multi-physics domain decomposition methods for time-dependent Stokes-Darcy systems


Authors: Yanzhao Cao, Max Gunzburger, Xiaoming He and Xiaoming Wang
Journal: Math. Comp. 83 (2014), 1617-1644
MSC (2010): Primary 65M55, 65M12, 65M15, 65M60, 35M10, 35Q35, 76D07, 76S05
Published electronically: February 3, 2014
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Abstract: Two parallel, non-iterative, multi-physics, domain decomposition methods are proposed to solve a coupled time-dependent Stokes-Darcy system with the Beavers-Joseph-Saffman-Jones interface condition. For both methods, spatial discretization is effected using finite element methods. The backward Euler method and a three-step backward differentiation method are used for the temporal discretization. Results obtained at previous time steps are used to approximate the coupling information on the interface between the Darcy and Stokes subdomains at the current time step. Hence, at each time step, only a single Stokes and a single Darcy problem need be solved; as these are uncoupled, they can be solved in parallel. The unconditional stability and convergence of the first method is proved and also illustrated through numerical experiments. The improved temporal convergence and unconditional stability of the second method is also illustrated through numerical experiments.


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Additional Information

Yanzhao Cao
Affiliation: Department of Mathematics and Statistics, Auburn University, Auburn, Alabama 36830
Email: yzc0009@auburn.edu

Max Gunzburger
Affiliation: Department of Scientific Computing, Florida State University, Tallahassee, Florida 32306
Email: gunzburg@fsu.edu

Xiaoming He
Affiliation: Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, Missouri 65409
Email: hex@mst.edu

Xiaoming Wang
Affiliation: Department of Mathematics, Florida State University, Tallahassee, Florida 32306
Email: wxm@math.fsu.edu

DOI: http://dx.doi.org/10.1090/S0025-5718-2014-02779-8
PII: S 0025-5718(2014)02779-8
Keywords: Stokes-Darcy model, domain decomposition methods, parallel algorithms, finite element methods
Received by editor(s): June 7, 2010
Received by editor(s) in revised form: July 22, 2012
Published electronically: February 3, 2014
Article copyright: © Copyright 2014 American Mathematical Society