Adaptive Double-Diffusion Model and Comparison to a Highly Heterogeneous Micro-Model

Adaptive Double-Diffusion Model and Comparison to a Highly Heterogeneous Micro-Model

Double-diffusion model is used to simulate slightly compressible fluid flow in periodic porous media as a macro-model in place of the original highly heterogeneous micro-model. In this paper, we formulate an adaptive two-grid numerical finite element discretization of the double-diffusion system and...

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Main Authors: Viviane Klein, Malgorzata Peszynska
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2012/938727
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spelling doaj-7711e9c0776c4cf59b98b0971bab47032020-11-24T22:28:56ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/938727938727Adaptive Double-Diffusion Model and Comparison to a Highly Heterogeneous Micro-ModelViviane Klein0Malgorzata Peszynska1Campus Araranguá, Universidade Federal de Santa Catarina, Rua Pedro João Pereira, 150, 88900-000 Araranguá, SC, BrazilDepartment of Mathematics, Oregon State University, 368 Kidder Hall, Corvallis, Oregon 97331-4605, USADouble-diffusion model is used to simulate slightly compressible fluid flow in periodic porous media as a macro-model in place of the original highly heterogeneous micro-model. In this paper, we formulate an adaptive two-grid numerical finite element discretization of the double-diffusion system and perform a comparison between the micro- and macro-model. Our numerical results show that the micro-model solutions appear to converge to the macro-model linearly with the parameter ε of periodic geometry. For the two-grid discretization, the a priori and a posteriori error estimates are proved, and we show how to adapt the grid for each component independently.http://dx.doi.org/10.1155/2012/938727
collection DOAJ
language English
format Article
sources DOAJ
author Viviane Klein
Malgorzata Peszynska
spellingShingle Viviane Klein
Malgorzata Peszynska
Adaptive Double-Diffusion Model and Comparison to a Highly Heterogeneous Micro-Model
Journal of Applied Mathematics
author_facet Viviane Klein
Malgorzata Peszynska
author_sort Viviane Klein
title Adaptive Double-Diffusion Model and Comparison to a Highly Heterogeneous Micro-Model
title_short Adaptive Double-Diffusion Model and Comparison to a Highly Heterogeneous Micro-Model
title_full Adaptive Double-Diffusion Model and Comparison to a Highly Heterogeneous Micro-Model
title_fullStr Adaptive Double-Diffusion Model and Comparison to a Highly Heterogeneous Micro-Model
title_full_unstemmed Adaptive Double-Diffusion Model and Comparison to a Highly Heterogeneous Micro-Model
title_sort adaptive double-diffusion model and comparison to a highly heterogeneous micro-model
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2012-01-01
description Double-diffusion model is used to simulate slightly compressible fluid flow in periodic porous media as a macro-model in place of the original highly heterogeneous micro-model. In this paper, we formulate an adaptive two-grid numerical finite element discretization of the double-diffusion system and perform a comparison between the micro- and macro-model. Our numerical results show that the micro-model solutions appear to converge to the macro-model linearly with the parameter ε of periodic geometry. For the two-grid discretization, the a priori and a posteriori error estimates are proved, and we show how to adapt the grid for each component independently.
url http://dx.doi.org/10.1155/2012/938727
work_keys_str_mv AT vivianeklein adaptivedoublediffusionmodelandcomparisontoahighlyheterogeneousmicromodel
AT malgorzatapeszynska adaptivedoublediffusionmodelandcomparisontoahighlyheterogeneousmicromodel
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