Journal of Scientific Computing

, Volume 74, Issue 2, pp 693–727 | Cite as

Discontinuous Finite Volume Element Method for a Coupled Non-stationary Stokes–Darcy Problem

Article
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Abstract

In this paper, a discontinuous finite volume element method was presented to solve the nonstationary Stokes–Darcy problem for the coupling fluid flow in conduits with porous media flow. The proposed numerical method is constructed on a baseline finite element family of discontinuous linear elements for the approximation of the velocity and hydraulic head, whereas the pressure is approximated by piecewise constant elements. The unique solvability of the approximate solution for the discrete problem is derived. Optimal error estimates of the semi-discretization and full discretization with backward Euler scheme in standard \(L^2\)-norm and broken \(H^1\)-norm are obtained for three discontinuous finite volume element methods (symmetric, non-symmetric and incomplete types). A series of numerical experiments are provided to illustrate the features of the proposed method, such as the optimal accuracy orders, mass conservation, capability to deal with complicated geometries, and applicability to the problems with realistic parameters.

Keywords

Non-stationary Stokes–Darcy Discontinuous finite volume element method Beavers–Joseph–Saffman–Jones condition Error estimates 
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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsXi’an Jiaotong UniversityXi’anPeople’s Republic of China
  2. 2.Department of Mathematics, School of Arts and SciencesShaanxi University of Science and TechnologyXi’anPeople’s Republic of China
  3. 3.Department of MathematicsBaoji University of Arts and SciencesBaojiPeople’s Republic of China
  4. 4.Department of Chemical & Petroleum Engineering, Schulich School of EngineeringUniversity of CalgaryAlbertaCanada

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