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EFFICIENT ANALYTIC SERIES SOLUTIONS FOR TWO–DIMENSIONAL POTENTIAL FLOW PROBLEMS
Author(s) -
GILL A. W.,
READ W. W.
Publication year - 1996
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/(sici)1097-0363(19960915)23:5<415::aid-fld430>3.0.co;2-1
Subject(s) - series (stratigraphy) , interpolation (computer graphics) , mathematics , laplace transform , laplace's equation , boundary (topology) , boundary value problem , range (aeronautics) , mathematical optimization , mathematical analysis , computer science , animation , paleontology , materials science , computer graphics (images) , composite material , biology
The solution of Laplace's equation for a wide range of spatial domains and boundary conditions is a valuable asset in the study of potential theory. Recently, classical analytic series techniques based on separation of variables have been modified to solve Laplace's equation with both irregular and free boundaries. Computationally the free boundary problem is reduced to an iterative sequence of curve‐fitting exercises. At each iteration the series coefficients for a known boundary problem are evaluated numerically. In this paper a new interpolation approach is presented for the estimation of the series coefficients. It has the advantages of providing a conceptually simpler view of the series technique and of estimating the series coefficients significantly faster than alternative approaches. Owing to the choice of basis functions in the truncated series solution, rigorous estimates of the error in the approximation are immediately available. A free boundary problem from steady hillside seepage with irregular boundaries will be used to illustrate the new technique.