Convergence of nonlinear finite volume schemes for two-phase porous media flow on general meshes. (7th October 2020)

• Record Type: Journal Article
• Authors: Agélas, Léo; Schneider, Martin; Enchéry, Guillaume; Flemisch, Bernd
• Is Part Of: IMA journal of numerical analysis. Volume 42:Number 1(2022)
• Page Start: 515
• Page End: 568
• Publication Date: 2020-10-07
• Subjects: two-phase flow -- porous medium -- monotone schemes -- finite volume methods -- convergence analysis; Numerical analysis -- Periodicals; 519.405
• DOI: 10.1093/imanum/draa064
• Languages: English
• ISSNs: 0272-4979

Abstract

Abstract: In this work we present an abstract finite volume discretization framework for incompressible immiscible two-phase flow through porous media. A priori error estimates are derived that allow us to prove the existence of discrete solutions and to establish the proof of convergence for schemes belonging to this framework. In contrast to existing publications the proof is not restricted to a specific scheme and it assumes neither symmetry nor linearity of the flux approximations. Two nonlinear schemes, namely a nonlinear two-point flux approximation and a nonlinear multipoint flux approximation, are presented, and some properties of these schemes, e.g. saturation bounds, are proven. Furthermore, the numerical behavior of these schemes (e.g. accuracy, coercivity, efficiency or saturation bounds) is investigated for different test cases for which the coercivity is checked numerically.