A robust linearization scheme for finite volume based discretizations for simulation of two-phase flow in porous media

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:289

Article

Radu, Florin Adrian¹  Nordbotten, Jan Martin¹  Pop, Iuliu Sorin^1,2  Kumar, Kundan^1,3 

[1] Univ Bergen, Dept Math, N-5020 Bergen, Norway

[2] Eindhoven Univ Technol, Dept Math & Comp Sci, NL-5600 MB Eindhoven, Netherlands

[3] Univ Texas Austin, ICES, Austin, TX 78712 USA

关键词: Two-phase flow;    Linearization schemes;    Finite volume;    MPFA;    Convergence analysis;   

DOI  :  10.1016/j.cam.2015.02.051

来源: Elsevier

【 摘 要 】

In this work we consider a mathematical model for two-phase flow in porous media. The fluids are assumed immiscible and incompressible and the solid matrix non-deformable. The mathematical model for the two-phase flow is written in terms of the global pressure and a complementary pressure (obtained by using the Kirchhoff transformation) as primary unknowns. For the spatial discretization, finite volumes have been used (more precisely the multi-point flux approximation method) and in time the backward Euler method has been employed. We present here a new linearization scheme for the nonlinear system arising after the temporal and spatial discretization. We show that the scheme is linearly convergent. Numerical experiments are presented that sustain the theoretical results. (C) 2015 The Authors. Published by Elsevier B.V.

【 授权许可】

Free