Convergence of nonlinear finite volume schemes for two-phase porous media flow on general meshes - Archive ouverte HAL Access content directly
Journal Articles IMA Journal of Numerical Analysis Year : 2022

Convergence of nonlinear finite volume schemes for two-phase porous media flow on general meshes

(1) , (2) , (1) , (2)
1
2

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.
Not file

Dates and versions

hal-03910986 , version 1 (22-12-2022)

Identifiers

Cite

Léo Agélas, Martin Schneider, Guillaume Enchéry, Bernd Flemisch. Convergence of nonlinear finite volume schemes for two-phase porous media flow on general meshes. IMA Journal of Numerical Analysis, 2022, 42 (1), pp.515-568. ⟨10.1093/imanum/draa064⟩. ⟨hal-03910986⟩
0 View
0 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More