International Journal for Multiscale Computational Engineering

ISSN for PRINT: 1543-1649

For Online Access

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2008, Volume6

Issue 1

114 pages

DOI: 10.1615/IntJMultCompEng.v6.i1

Issue price - $150.00

Shuyu Sun
Department of Mathematical Sciences, Clemson University, Clemson, SC 29634-0975, USA

Juergen Geiser
Department of Mathematics, Humboldt University of Berlin

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.

DOI: 10.1615/IntJMultCompEng.v6.i1.80 Download article, 87-101 pages

Article price - $35.00

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