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International Journal for Multiscale Computational Engineering
IF: 1.016 5-Year IF: 1.194 SJR: 0.554 SNIP: 0.82 CiteScore™: 2

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

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

Multiscale Discontinuous Galerkin and Operator-Splitting Methods for Modeling Subsurface Flow and Transport

Shuyu Sun
School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, P.R. China 710049; Computational Transport Phenomena Laboratory, Division of Physical Science and Engineering, King Abdullah University of Science and Technology, Thuwal 23955-6900, Kingdom of Saudi Arabia
Juergen Geiser
Univerity of Greifswald

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.


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