Permeability Models for Magma Flow through the Earth's Mantle: A Lie Group Analysis

Permeability Models for Magma Flow through the Earth's Mantle: A Lie Group Analysis

The migration of melt through the mantle of the Earth is governed by a third-order nonlinear partial differential equation for the voidage or volume fraction of melt. The partial differential equation depends on the permeability of the medium which is assumed to be a function of the voidage. It is s...

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Main Authors: N. Mindu, D. P. Mason
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2013/258528
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spelling doaj-afdc6ca4395c4ae49cc1e9de8258c18e2020-11-24T22:57:42ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/258528258528Permeability Models for Magma Flow through the Earth's Mantle: A Lie Group AnalysisN. Mindu0D. P. Mason1Centre for Differential Equations, Continuum Mechanics and Applications and School of Computational and Applied Mathematics, University of the Witwatersrand, Johannesburg, Private Bag 3, Wits 2050, South AfricaCentre for Differential Equations, Continuum Mechanics and Applications and School of Computational and Applied Mathematics, University of the Witwatersrand, Johannesburg, Private Bag 3, Wits 2050, South AfricaThe migration of melt through the mantle of the Earth is governed by a third-order nonlinear partial differential equation for the voidage or volume fraction of melt. The partial differential equation depends on the permeability of the medium which is assumed to be a function of the voidage. It is shown that the partial differential equation admits, as well as translations in time and space, other Lie point symmetries provided the permeability is either a power law or an exponential law of the voidage or is a constant. A rarefactive solitary wave solution of the partial differential equation is derived in the form of a quadrature for the exponential law for the permeability.http://dx.doi.org/10.1155/2013/258528
collection DOAJ
language English
format Article
sources DOAJ
author N. Mindu
D. P. Mason
spellingShingle N. Mindu
D. P. Mason
Permeability Models for Magma Flow through the Earth's Mantle: A Lie Group Analysis
Journal of Applied Mathematics
author_facet N. Mindu
D. P. Mason
author_sort N. Mindu
title Permeability Models for Magma Flow through the Earth's Mantle: A Lie Group Analysis
title_short Permeability Models for Magma Flow through the Earth's Mantle: A Lie Group Analysis
title_full Permeability Models for Magma Flow through the Earth's Mantle: A Lie Group Analysis
title_fullStr Permeability Models for Magma Flow through the Earth's Mantle: A Lie Group Analysis
title_full_unstemmed Permeability Models for Magma Flow through the Earth's Mantle: A Lie Group Analysis
title_sort permeability models for magma flow through the earth's mantle: a lie group analysis
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2013-01-01
description The migration of melt through the mantle of the Earth is governed by a third-order nonlinear partial differential equation for the voidage or volume fraction of melt. The partial differential equation depends on the permeability of the medium which is assumed to be a function of the voidage. It is shown that the partial differential equation admits, as well as translations in time and space, other Lie point symmetries provided the permeability is either a power law or an exponential law of the voidage or is a constant. A rarefactive solitary wave solution of the partial differential equation is derived in the form of a quadrature for the exponential law for the permeability.
url http://dx.doi.org/10.1155/2013/258528
work_keys_str_mv AT nmindu permeabilitymodelsformagmaflowthroughtheearthsmantlealiegroupanalysis
AT dpmason permeabilitymodelsformagmaflowthroughtheearthsmantlealiegroupanalysis
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