• Home
  1. Home
  2. Convergence of Implicit Monotone Schemes with Applications in Multiphase Flow in Porous Media
Scientific article
OA Policy
English

Convergence of Implicit Monotone Schemes with Applications in Multiphase Flow in Porous Media

Contributors

Kwok, Wing Hong Félix; Tchelepi, Hamdi A.

Published in

SIAM journal on numerical analysis, vol. 46, no. 5, p. 2662-2687

Publication date

2008

Abstract

Phase-based upstreaming, which is a commonly used spatial discretization for multiphase flow in reservoir simulation, naturally gives rise to implicit monotone schemes when implicit time-stepping is used. The nonlinear Gauss–Seidel and Jacobi algorithms are shown to converge to a unique bounded solution when applied to the resulting system of equations. Thus, for one-dimensional problems, we obtain an alternate, constructive proof that such schemes are well-defined and converge to the entropy solution of the conservation law for arbitrary CFL numbers. The accuracy of phase-based upstream solutions is studied for various spatial and temporal grids, revealing the importance of unconditional stability when nonuniform grids and/or variable porosity is involved.

UNIGE affiliation entities

Citation (ISO format)

KWOK, Wing Hong Félix, TCHELEPI, Hamdi A. Convergence of Implicit Monotone Schemes with Applications in Multiphase Flow in Porous Media. In: SIAM journal on numerical analysis, 2008, vol. 46, n° 5, p. 2662–2687. doi: 10.1137/070703922

Main files (1)

Article (Published version)

Identifiers

Journal ISSN

0036-1429
592views
603downloads

Technical informations

Creation

02/07/2010 14:00:00

First validation

02/07/2010 14:00:00

Update

14/03/2023 15:49:43

Status update

14/03/2023 15:49:43

Last indexation

29/10/2024 15:43:24
All rights reserved by Archive ouverte UNIGE and the University of Geneva
OpenAIRE Indexed & Validated