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Finite difference approximation of boundary conditions along irregular boundaries
Author(s) -
Hunt Bruce
Publication year - 1978
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/nme.1620120205
Subject(s) - boundary (topology) , simple (philosophy) , finite difference , mathematics , boundary value problem , finite difference method , mathematical analysis , geometry , epistemology , philosophy
The approximation of normal derivatives along a curved boundary becomes a major difficulty in obtaining finite difference solutions for irregular regions. A number of authors (for‐example, Allen, 1 Fox, 2 Greenspan 3 and Parker and Ma 4 ) have suggested various solutions to this problem. However, most of these suggested methods are fairly cumbersome to use since they require the use of different formulas for various combinations of mesh and boundary geometries. This note shows a different way to approximate a quite general boundary condition along curved boundaries. The method uses a uniformly spaced mesh, is simple, general, relatively easy to program and appears to give accurate results.