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Transformation of elliptic partial differential equations for solving two‐dimensional boundary value problems in fluid flow
Author(s) -
Boadway J. D.
Publication year - 1976
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.1620100304
Subject(s) - streamlines, streaklines, and pathlines , partial differential equation , mathematics , position (finance) , elliptic partial differential equation , boundary value problem , mathematical analysis , stream function , flow (mathematics) , laplace's equation , free boundary problem , first order partial differential equation , function (biology) , boundary (topology) , geometry , physics , mechanics , vorticity , evolutionary biology , vortex , economics , biology , finance
It is possible to transform elliptic partial differential equations to exchange the dependent with one of the independent variables. The Laplace equation for a stream function ‘Ψ’ over the X and Y co‐ordinate system, for example, can be transformed into a relationship expressing the Y position of streamlines in terms of strem function Ψ and X . Although the resulting new partial differential equation is much more complex it is much more convenient to use in a computer. An irregular Y boundary becomes, with the new relationship, merely the boundary values assigned to the outer streamlines and the computer always need only deal with a rectangular array. The resulting answer is in the form of the position of streamlines which is the information directly required for plotting flow maps.