The boundary element method applied to a moving free boundary problem

In this paper a boundary problem is considered for which the boundary is to be determined as part of the solution. A time‐dependent problem involving linear diffusion in two spatial dimensions which results in a moving free boundary is posed. The fundamental solution is introduced and Green’s Theore...

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Bibliographic Details
Published inInternational journal for numerical methods in engineering Vol. 46; no. 8; pp. 1335 - 1346
Main Authors Quinn, Dennis W., Oxley, Mark E., Vosika, Donald C.
Format Journal Article
LanguageEnglish
Published Chichester, UK John Wiley & Sons, Ltd 20.11.1999
Subjects
boundary element method
contaminant transport
diffusion equation
free boundary
moving boundary
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Summary:In this paper a boundary problem is considered for which the boundary is to be determined as part of the solution. A time‐dependent problem involving linear diffusion in two spatial dimensions which results in a moving free boundary is posed. The fundamental solution is introduced and Green’s Theorem is used to yield a non‐linear system of integral equations for the unknown solution and the location of the boundary. The boundary element method is used to obtain a numerical solution to this system of integral equations which in turn is used to obtain the solution of the original problem. Graphical results for a two‐dimensional problem are presented. Published in 1999 by John Wiley & Sons, Ltd.
Bibliography:This article is a U.S. Government work and is in the public domain in the U.S.A.
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ISSN:0029-5981
1097-0207
DOI:10.1002/(SICI)1097-0207(19991120)46:8<1335::AID-NME757>3.0.CO;2-9