A strongly conservative finite element method for the coupling of Stokes and Darcy flow
We consider a model of coupled free and porous media flow governed by Stokes and Darcy equations with the Beavers–Joseph–Saffman interface condition. This model is discretized using divergence-conforming finite elements for the velocities in the whole domain. Discontinuous Galerkin techniques and mi...
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| Published in | Journal of computational physics Vol. 229; no. 17; pp. 5933 - 5943 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Kidlington
Elsevier Inc
20.08.2010
Elsevier |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0021-9991 1090-2716 |
| DOI | 10.1016/j.jcp.2010.04.021 |
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| Abstract | We consider a model of coupled free and porous media flow governed by Stokes and Darcy equations with the Beavers–Joseph–Saffman interface condition. This model is discretized using divergence-conforming finite elements for the velocities in the whole domain. Discontinuous Galerkin techniques and mixed methods are used in the Stokes and Darcy subdomains, respectively. This discretization is strongly conservative in
H
div(
Ω) and we show convergence. Numerical results validate our findings and indicate optimal convergence orders. |
|---|---|
| AbstractList | We consider a model of coupled free and porous media flow governed by Stokes and Darcy equations with the Beavers-Joseph-Saffman interface condition. This model is discretized using divergence-conforming finite elements for the velocities in the whole domain. Discontinuous Galerkin techniques and mixed methods are used in the Stokes and Darcy subdomains, respectively. This discretization is strongly conservative in H super(div)([Omega]) and we show convergence. Numerical results validate our findings and indicate optimal convergence orders. We consider a model of coupled free and porous media flow governed by Stokes and Darcy equations with the Beavers–Joseph–Saffman interface condition. This model is discretized using divergence-conforming finite elements for the velocities in the whole domain. Discontinuous Galerkin techniques and mixed methods are used in the Stokes and Darcy subdomains, respectively. This discretization is strongly conservative in H div( Ω) and we show convergence. Numerical results validate our findings and indicate optimal convergence orders. |
| Author | Rivière, B. Kanschat, G. |
| Author_xml | – sequence: 1 givenname: G. surname: Kanschat fullname: Kanschat, G. email: kanschat@tamu.edu organization: Department of Mathematics, Texas A&M University, 3368 TAMU, College Station, TX 77843-3368, United States – sequence: 2 givenname: B. surname: Rivière fullname: Rivière, B. organization: Department of Computational and Applied Mathematics, Rice University, 6100 Main Street, MS-134, Houston, TX 77005-1892, United States |
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| Keywords | Finite element method Multiphysics Discontinuous Galerkin Beavers–Joseph–Saffman condition Stokes flow Darcy flow Mixed finite elements Stokes equation Porous medium Calculation methods Divergences Beavers-Joseph-Saffman condition Discretization Models Calculation |
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| Snippet | We consider a model of coupled free and porous media flow governed by Stokes and Darcy equations with the Beavers–Joseph–Saffman interface condition. This... We consider a model of coupled free and porous media flow governed by Stokes and Darcy equations with the Beavers-Joseph-Saffman interface condition. This... |
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| SubjectTerms | Beavers–Joseph–Saffman condition Computational fluid dynamics Computational techniques Convergence Darcy flow Discontinuous Galerkin Exact sciences and technology Finite element method Fluid flow Galerkin methods Mathematical analysis Mathematical methods in physics Mathematical models Mixed finite elements Multiphysics Physics Stokes flow Stokes law (fluid mechanics) |
| Title | A strongly conservative finite element method for the coupling of Stokes and Darcy flow |
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