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Modeling potential flow using Laurent series expansions and boundary elements
Author(s) -
Dean T.R.,
Hromadka T.V.,
Kastner Thomas,
Phillips Michael
Publication year - 2012
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20636
Subject(s) - mathematics , bernoulli's principle , laurent series , partial differential equation , flow (mathematics) , mathematical analysis , boundary value problem , power series , boundary (topology) , series (stratigraphy) , domain (mathematical analysis) , geometry , paleontology , engineering , biology , aerospace engineering
The fundamental underpinnings of the well‐known Bernoulli's Equation, as used to describe steady state two‐dimensional flow of an ideal incompressible irrotational flow, are typically described in terms of partial differential equations. However, it has been shown that the Cauchy Integral Theorem of standard complex variables also explain the Bernoulli's Equation and, hence, can be directly used to model problems of ideal fluid flow (or other potential problems such as electrostatics among other topics) using approximation function techniques such as the complex variable boundary element method (CVBEM). In this article, the CVBEM is extended to include Laurent Series expansions about singular points located outside of the problem domain union boundary. It is shown that by including such negatively powered complex monomials in the CVBEM formulation, considerable power is introduced to model potential flow problems. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 573–586,2012