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Short Communication: A numerical method for diffusive transport with moving boundaries and discontinuous material properties
Author(s) -
Li Zhilin,
McTigue David F.,
Heine Jan T.
Publication year - 1997
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/(sici)1096-9853(199709)21:9<653::aid-nag894>3.0.co;2-5
Subject(s) - classification of discontinuities , discontinuity (linguistics) , convection–diffusion equation , convection , mechanics , benchmark (surveying) , mathematical analysis , thermal , diffusion , variable (mathematics) , geology , mathematics , physics , thermodynamics , geodesy
A method for the numerical simulation of diffusive transport with moving boundaries is developed and tested. The variable domain is mapped onto a fixed region, which introduces a term of convective form to the transformed governing equation. The resulting convection/diffusion equation is solved by a finite‐difference method. An ‘Immersed Interface’ Method (IIM) is introduced in order to retain second‐order accuracy near discontinuities in material properties, where the solution is not smooth. The method performs well in benchmark calculations against an analytical solution. The IIM scheme is capable of treating a strong discontinuity in the gradient, and it is readily extended to two or three dimensions. The methods are illustrated through a calculation for the temperature profile in a growing continental ice sheet, in which the thermal properties are discontinuous at the rock/ice interface. © 1997 by John Wiley & Sons, Ltd.