Multiscale discontinuous Galerkin and operator-splitting methods for modeling subsurface flow and transport

Shuyu Sun*, Jurgen Geiser

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

Multiscale algorithms are considered for solving flow and transport problems in geological media. Challenges of multiscale permeability variation in subsurface flow problems are addressed by using multiscale discontinuous Galerkin (DG) methods, where we construct local DG basis functions at a coarse scale while capturing local properties of Darcy flow at a fine scale, and then solve the DG formulation using the newly constructed local basis functions on the coarse-scale elements. Challenges of transport problems include the coupling of multiple processes, such advection, diffusion, dispersion, and reaction across different scales, which is treated here by using two splitting approaches based on operator decomposition. The methods decompose the coupled system into various individual operators with respect to their scales and physics, so that each subproblem can be solved with its own most efficient algorithm. These subproblems are coupled adaptively with iterative steps. Error estimates for the decomposition methods are derived. Numerical examples are provided to demonstrate the properties and effectiveness of both multiscale DG and operator-splitting methods.

Original languageEnglish (US)
Pages (from-to)87-101
Number of pages15
JournalInternational Journal for Multiscale Computational Engineering
Volume6
Issue number1
DOIs
StatePublished - Apr 1 2008

Keywords

  • Convection-diffusion-reaction equations
  • Discontinuous Galerkin methods
  • Flow in porous media
  • Multiscale methods
  • Operator splitting

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computational Mechanics
  • Computer Networks and Communications

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