Analysis of a Second-Order, Unconditionally Stable, Partitioned Method for the Evolutionary Stokes-Darcy Model
Year: 2015
International Journal of Numerical Analysis and Modeling, Vol. 12 (2015), Iss. 4 : pp. 704–730
Abstract
We propose and analyze a partitioned numerical method for the fully evolutionary Stokes-Darcy equations that model the coupling between surface and groundwater flows. The proposed method uncouples the surface from the groundwater flow by using the implicit-explicit combination of the Crank-Nicolson and Leapfrog methods for the discretization in time with added stabilization terms. We prove that the method is asymptotically, unconditionally stable — requiring no time step condition — and second-order accurate in time with optimal rates in space. We verify the method's unconditional stability and second-order accuracy numerically.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2015-IJNAM-508
International Journal of Numerical Analysis and Modeling, Vol. 12 (2015), Iss. 4 : pp. 704–730
Published online: 2015-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 27
Keywords: Stokes Darcy groundwater surface water partitioned decoupled second-order accuracy unconditional stability asymptotic stability.