NDLI: Efficient and Long-Time Accurate Second-Order Methods for the Stokes--Darcy System

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Chen, Wenbin Gunzburger, Max Sun, Dong Wang, Xiaoming
Copyright Year	2013
Abstract	We propose and study two second-order in time implicit-explicit methods for the coupled Stokes--Darcy system that governs flows in karst aquifers and other subsurface flow systems. The first method is a combination of a second-order backward differentiation formula and the second-order Gear's extrapolation approach. The second is a combination of the second-order Adams--Moulton and second-order Adams--Bashforth methods. Both algorithms only require the solution of decoupled Stokes and Darcy problems at each time-step. Hence, these schemes are very efficient and can be easily implemented using legacy codes. We establish the unconditional and uniform in time stability for both schemes. The uniform in time stability leads to uniform in time control of the error which is highly desirable for modeling physical processes, e.g., contaminant sequestration and release, that occur over very long time scales. Error estimates for fully discretized schemes using finite element spatial discretizations are derived. Numerical examples are provided that illustrate the accuracy, efficiency, and long-time stability of the two schemes.
Starting Page	2563
Ending Page	2584
Page Count	22
File Format	PDF
ISSN	00361429
DOI	10.1137/120897705
e-ISSN	10957170
Issue Number	5
Volume Number	51
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2013-09-10
Access Restriction	Subscribed
Subject Keyword	Gear's extrapolation long-time stability PDEs in connection with fluid mechanics Initial-boundary value problems for equations of mixed type unconditional stability backward differentiation formulas Stokes and related (Oseen, etc.) flows uniform in time error estimates Flows in porous media; filtration; seepage Stokes--Darcy systems Adams--Moulton and Adams--Bashforth methods karst aquifers finite element methods Multigrid methods; domain decomposition Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Numerical Analysis Computational Mathematics

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