A coarsening multigrid method for flow in heterogeneous porous media

Jens Eberhard, Gabriel Wittum

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

7 Scopus citations


This paper focuses on multigrid methods for flow in heterogeneous porous media. We consider Darcy flow and the local permeability K(x) being a stationary random field of lognormal distribution. We apply the recently developed coarse graining method for the numerical upscaling of permeability, and develop a new multigrid method which applies this technique to obtain the coarse grid operators. The coarse grid operators are adjusted to the scale-dependent behaviour of the system as it incorporates only fluctuations of K on larger scales. This kind of action is essential for an efficient interplay with simple smoothers. We investigate important properties of the new multigrid method such as dependence on the boundary conditions and on grid refinement for the coarse graining and dependence on the mesh size. We compare the resulting method with the algebraic method of Ruge and Stüben, a Schurcomplement method, and matrix-dependent multigrid methods by solving the flow equation with K being random realizations as well as periodic media. The numerical convergence rates show that the new method is as efficient as the algebraic methods for variances σ2f ≤ 3 of K.

Original languageEnglish (US)
Title of host publicationMultiscale Methods in Science and Engineering
Number of pages22
StatePublished - 2005
Externally publishedYes

Publication series

NameLecture Notes in Computational Science and Engineering
ISSN (Print)1439-7358


  • Heterogeneity
  • Multigrid method
  • Porous media
  • Upscaling

ASJC Scopus subject areas

  • Modeling and Simulation
  • General Engineering
  • Discrete Mathematics and Combinatorics
  • Control and Optimization
  • Computational Mathematics


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