Convergence analysis of a DDFV scheme for a system describing miscible fluid flows in porous media. Issue 3 (14th August 2014)

• Record Type: Journal Article
• Authors: Chainais‐Hillairet, Claire; Krell, Stella; Mouton, Alexandre
• Is Part Of: Numerical methods for partial differential equations. Volume 31:Issue 3(2015)
• Page Start: 723
• Page End: 760
• Publication Date: 2014-08-14
• Subjects: finite volume method -- convergence analysis -- porous medium -- miscible fluid flows; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.21913
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract : In this article, we prove the convergence of a discrete duality finite volume scheme for a system of partial differential equations describing miscible displacement in porous media. This system is made of two coupled equations: an anisotropic diffusion equation on the pressure and a convection‐diffusion‐dispersion equation on the concentration. We first establish some a priori estimates satisfied by the sequences of approximate solutions. Then, it yields the compactness of these sequences. Passing to the limit in the numerical scheme, we finally obtain that the limit of the sequence of approximate solutions is a weak solution to the problem under study. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 723–760, 2015