An efficient and long-time accurate third-order algorithm for the Stokes–Darcy system

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• 作者：Wenbin Chen ; Max Gunzburger ; Dong Sun ; Xiaoming Wang
• 关键词：Mathematics Subject Classification35M13 ; 35Q35 ; 65N30 ; 65N55 ; 76D07 ; 76S05
• 刊名：Numerische Mathematik
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：134
• 期：4
• 页码：857-879
• 全文大小：719 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Numerical Analysis
  Mathematics
  Mathematical and Computational Physics
  Mathematical Methods in Physics
  Numerical and Computational Methods
  Applied Mathematics and Computational Methods of Engineering
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：0945-3245
• 卷排序：134

文摘

A third-order in time numerical IMEX-type algorithm for the Stokes–Darcy system for flows in fluid saturated karst aquifers is proposed and analyzed. A novel third-order Adams–Moulton scheme is used for the discretization of the dissipative term whereas a third-order explicit Adams–Bashforth scheme is used for the time discretization of the interface term that couples the Stokes and Darcy components. The scheme is efficient in the sense that one needs to solve, at each time step, decoupled Stokes and Darcy problems. Therefore, legacy Stokes and Darcy solvers can be applied in parallel. The scheme is also unconditionally stable and, with a mild time-step restriction, long-time accurate in the sense that the error is bounded uniformly in time. Numerical experiments are used to illustrate the theoretical results. To the authors’ knowledge, the novel algorithm is the first third-order accurate numerical scheme for the Stokes–Darcy system possessing its favorable efficiency, stability, and accuracy properties.