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Multiscale modelling and computation of fluid flow
Author(s) -
Hou Thomas Y.
Publication year - 2005
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.866
Subject(s) - partial differential equation , computation , computer science , nonlinear system , flow (mathematics) , multiscale modeling , porous medium , mathematics , scale (ratio) , mathematical optimization , fluid dynamics , statistical physics , algorithm , mechanics , physics , mathematical analysis , geology , geometry , porosity , chemistry , computational chemistry , geotechnical engineering , quantum mechanics
Many problems of fundamental and practical importance have multiscale solutions. Direct numerical simulation of these multiscale problems is difficult due to the range of length scales in the underlying physical problems. Here, we describe two multiscale methods for computing nonlinear partial differential equations with multiscale solutions. The first method relies on constructing local multiscale bases for diffusion‐dominated problems. We demonstrate that such an approach can be used to upscale two‐phase flow in heterogeneous porous media. The second method is to construct semi‐analytic multiscale solutions local in space and time. We use these solutions to approximate the large‐scale solution for convection‐dominated transport. This approach overcomes the common difficulty due to the memory effect in deriving the averaged equations for convection‐dominated transport. Our multiscale analysis provides a useful guideline for designing effective numerical methods for incompressible flow. Copyright © 2005 John Wiley & Sons, Ltd.