Convergence analysis of an approximation to miscible fluid flows in porous media by combining mixed finite element and finite volume methods
✍ Scribed by Brahim Amaziane; Mustapha El Ossmani
- Publisher
- John Wiley and Sons
- Year
- 2008
- Tongue
- English
- Weight
- 751 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0749-159X
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
This article deals with development and analysis of a numerical method for a coupled system describing miscible displacement of one incompressible fluid by another through heterogeneous porous media. A mixed finite element (MFE) method is employed to discretize the Darcy flow equation combined with a conservative finite volume (FV) method on unstructured grids for the concentration equation. It is shown that the FV scheme satisfies a discrete maximum principle. We derive L^∞^ and BV estimates under an appropriate CFL condition. Then we prove convergence of the approximate solutions to a weak solution of the coupled system. Numerical results are presented to see the performance of the method in two space dimensions. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008