Study of a numerical scheme for miscible two‐phase flow in porous media. Issue 3 (11th December 2013)

• Record Type: Journal Article
• Authors: Eymard, Robert; Schleper, Veronika
• Is Part Of: Numerical methods for partial differential equations. Volume 30:Issue 3(2014:May)
• Page Start: 723
• Page End: 748
• Publication Date: 2013-12-11
• Subjects: Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.21823
• Languages: English
• ISSNs: 0749-159X

Abstract

<abstract abstract-type="main"> <title> <x xml:space="preserve">Abstract</x> </title> <p>We study the convergence of a finite volume scheme for a model of miscible two‐phase flow in porous media. In this model, one phase can dissolve into the other one. The convergence of the scheme is proved thanks to an estimate on the two pressures, which allows to prove some estimates on the discrete time derivative of some nonlinear functions of the unknowns. Monotony arguments allow to show some properties on the limits of these functions. A key point in the scheme is to use particular averaging formula for the dissolution function arising in the space term. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 723–748, 2014</p> </abstract>