A decoupling method with different subdomain time steps for the nonstationary stokes–darcy model. Issue 2 (18th April 2012)

• Record Type: Journal Article
• Authors: Shan, Li; Zheng, Haibiao; Layton, William J.
• Is Part Of: Numerical methods for partial differential equations. Volume 29:Issue 2(2013:Mar.)
• Page Start: 549
• Page End: 583
• Publication Date: 2012-04-18
• Subjects: Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.21720
• Languages: English
• ISSNs: 0749-159X

Abstract

<abstract abstract-type="main" xml:lang="en"> <title>Abstract</title> <p>This report analyzes a multirate, decoupling algorithm, which allows different time steps in the fluid region and the porous region for the nonstationary Stokes–Darcy problem. The method presented requires only one, uncoupled Stokes and Darcy subphysics and subdomain solve per time step. Under a time step restriction of the form △<italic>t</italic> ≤ <italic>C</italic> (physical parameters) we prove stability and convergence of the method. Numerical tests are given to show the convergence result and demonstrate the computational efficiency of the partitioned method. They also show that in the expected case of greater fluid velocities in the free‐flow region than in the porous media region, allowing smaller time steps in the subregion with the faster velocities increases both accuracy and efficiency. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013</p> </abstract>