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Портал Begell Электронная Бибилиотека e-Книги Журналы Справочники и Сборники статей Коллекции
International Journal for Multiscale Computational Engineering
Импакт фактор: 1.016 5-летний Импакт фактор: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN Печать: 1543-1649
ISSN Онлайн: 1940-4352

Выпуски:
Том 17, 2019 Том 16, 2018 Том 15, 2017 Том 14, 2016 Том 13, 2015 Том 12, 2014 Том 11, 2013 Том 10, 2012 Том 9, 2011 Том 8, 2010 Том 7, 2009 Том 6, 2008 Том 5, 2007 Том 4, 2006 Том 3, 2005 Том 2, 2004 Том 1, 2003

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

Краткое описание

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.