Adaptive numerical homogenization for upscaling single phase flow and transport

Yerlan Amanbek, Gurpreet Singh, Mary F. Wheeler, Hans van Duijn

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


We propose an adaptive multiscale method to improve the efficiency and the accuracy of numerical computations by combining numerical homogenization and domain decomposition for modeling flow and transport. Our approach focuses on minimizing the use of fine scale properties associated with advection and diffusion/dispersion. Here a fine scale flow and transport problem is solved in subdomains defined by a transient region where spatial changes in transported species concentrations are large while a coarse scale problem is solved in the remaining subdomains. Away from the transient region, effective macroscopic properties are obtained using local numerical homogenization. An Enhanced Velocity Mixed Finite Element Method (EVMFEM) as a domain decomposition scheme is used to couple these coarse and fine subdomains [1]. Specifically, homogenization is employed here only when coarse and fine scale problems can be decoupled to extract temporal invariants in the form of effective parameters. In this paper, a number of numerical tests are presented for demonstrating the capabilities of this adaptive numerical homogenization approach in upscaling flow and transport in heterogeneous porous medium.

Original languageEnglish
Pages (from-to)117-133
Number of pages17
JournalJournal of Computational Physics
Publication statusPublished - Jun 15 2019


  • Adaptive mesh refinement
  • Enhanced velocity
  • Multiscale methods
  • Numerical homogenization

ASJC Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Adaptive numerical homogenization for upscaling single phase flow and transport'. Together they form a unique fingerprint.

Cite this