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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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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Abstract 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.
AbstractList The possibility of using the boundary element method to solve moving free boundary value problems is demonstrated. The problem examined relates to contaminant transport in a porous medium. The technique extends to higher dimensions and to some problems with nonlinearities included in the boundary conditions. (AIAA)
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.
Author Oxley, Mark E.
Vosika, Donald C.
Quinn, Dennis W.
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Cites_doi 10.1007/978-3-642-48860-3
10.2514/3.6038
10.1002/cpa.3160090102
10.1016/S0955-7997(96)00034-3
10.1002/nme.1620350111
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Snippet 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...
The possibility of using the boundary element method to solve moving free boundary value problems is demonstrated. The problem examined relates to contaminant...
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StartPage 1335
SubjectTerms boundary element method
contaminant transport
diffusion equation
free boundary
moving boundary
Title The boundary element method applied to a moving free boundary problem
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