Computational Geosciences

, Volume 15, Issue 1, pp 3–16

Monotonicity for MPFA methods on triangular grids

Original Paper

DOI: 10.1007/s10596-010-9191-5

Cite this article as:
Keilegavlen, E. & Aavatsmark, I. Comput Geosci (2011) 15: 3. doi:10.1007/s10596-010-9191-5


Flow in a porous medium can be described by a set of non-linear partial differential equations. The pressure variable satisfies a maximum principle, which guarantees that the solution will have no oscillations. A discretisation of the pressure equation should preserve this monotonicity property. Whether a numerical method is monotone will depend both on the medium and on the grid. We study monotonicity of Multi-point Flux Approximation methods on triangular grids. We derive necessary conditions for monotonicity on uniform grids. Further, we study the robustness of the methods on rough grids, and quantify the violations of the maximum principle. These investigations are done for single phase flow, however, they are supported by two-phase simulations.


MonotonicityMPFA methodsTriangular gridsElliptic conservation laws

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Centre for Integrated Petroleum Research (CIPR), UiB, Department of MathematicsUniversity of Bergen (UiB)BergenNorway
  2. 2.CIPRBergenNorway