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The boundary element method applied to a moving free boundary problem
Author(s) -
Quinn Dennis W.,
Oxley Mark E.,
Vosika Donald C.
Publication year - 1999
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19991120)46:8<1335::aid-nme757>3.0.co;2-9
Subject(s) - boundary element method , boundary knot method , singular boundary method , free boundary problem , mathematics , method of fundamental solutions , boundary (topology) , mathematical analysis , mixed boundary condition , boundary value problem , boundary problem , robin boundary condition , finite element method , engineering , structural engineering
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.