Analysis of time-dependent Navier–Stokes flow coupled with Darcy flow
- 1 January 2008
- journal article
- research article
- Published by Walter de Gruyter GmbH in Journal of Numerical Mathematics
- Vol. 16 (4), 249-280
- https://doi.org/10.1515/jnum.2008.012
Abstract
This paper formulates and analyzes a weak solution to the coupling of time-dependent Navier–Stokes flow with Darcy flow under certain boundary conditions, one of them being the Beaver–Joseph–Saffman law on the interface. Existence and a priori estimates for the weak solution are shown under additional regularity assumptions. We introduce a fully discrete scheme with the unknowns being the Navier–Stokes velocity, pressure and the Darcy pressure. The scheme we propose is based on a finite element method in space and a Crank–Nicolson discretization in time where we obtain the solution at the first time step using a first order backward Euler method. Convergence of the scheme is obtained and optimal error estimates with respect to the mesh size are derived.Keywords
This publication has 11 references indexed in Scilit:
- A computational method for approximating a Darcy–Stokes system governing a vuggy porous mediumComputational Geosciences, 2007
- A Two-Grid Method of a Mixed Stokes–Darcy Model for Coupling Fluid Flow with Porous Media FlowSIAM Journal on Numerical Analysis, 2007
- Robin–Robin Domain Decomposition Methods for the Stokes–Darcy CouplingSIAM Journal on Numerical Analysis, 2007
- A unified stabilized method for Stokes’ and Darcy's equationsJournal of Computational and Applied Mathematics, 2007
- Numerical Analysis of Coupled Stokes/Darcy Flows in Industrial FiltrationsTransport in Porous Media, 2006
- Analysis of a Discontinuous Finite Element Method for the Coupled Stokes and Darcy ProblemsJournal of Scientific Computing, 2005
- Mathematical and numerical models for coupling surface and groundwater flowsApplied Numerical Mathematics, 2002
- Coupling Fluid Flow with Porous Media FlowSIAM Journal on Numerical Analysis, 2002
- A stable finite element for the stokes equationsCalcolo, 1984
- Boundary conditions at a naturally permeable wallJournal of Fluid Mechanics, 1967