Coarse graining for upscaling of flow in heterogeneous porous media

Jens Eberhard, Sabine Attinger, Gabriel Wittum

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


This paper focuses on upscaling of permeability and flow in heterogeneous porous media. We develop a new upscaling method which considers the local permeability K(x) being a stationary random field of lognormal distribution and which is based on filtering procedures introduced in Attinger, Eberhard, and Neuss [Comput. Vis. Sci., 5 (2002), pp. 67-72]. The so-called coarse graining method is used to obtain an effective permeability tensor Keff(λ) which depends on the given length scale λ. We formulate and extend the coarse graining method in Fourier space and give explicit results for the effective permeability tensor for a correct projector P ± λ in Fourier space. Furthermore, we develop a numerical upscaling scheme based on coarse graining which allows us to test the theoretical results. We compare the new method with simple upscaling methods such as arithmetic or geometric upscaling by evaluating fluxes Qλ and the solutions uλ of the flow equation itself for varying length scales 1/4 ≤ λ/l0 ≤ 16. In all cases the numerical coarse graining proves best.

Original languageEnglish (US)
Pages (from-to)269-301
Number of pages33
JournalMultiscale Modeling and Simulation
Issue number2
StatePublished - 2004
Externally publishedYes


  • Effective permeability
  • Heterogeneity
  • Porous media
  • Upscaling

ASJC Scopus subject areas

  • General Chemistry
  • Modeling and Simulation
  • Ecological Modeling
  • General Physics and Astronomy
  • Computer Science Applications


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