The Complex Variable Boundary Element
Method For Potential Flow Problems
Author(s)
M. Mokry
Abstract
The Cauchy type integral, used to represent the complex velocity, is converted to
a line distribution of sources and vortices in the complex plane. The specification
of the normal velocity on the bounding contour leads to a Riemann-Hilbert problem,
which provides the theoretical foundation of the method. The boundary element
discretization results in a simple algorithm for calculating potential flows in
multiple-connected domains. Flow problems with periodic or homogeneous outer
boundary conditions are treated using the concept of the Green’s function in the
complex plane.
1 Introduction
The Complex Variable Boundary ElementMethod (CVBEM) evolved as a numerical
procedure for solving boundary value problems for analytic functions in terms
of discretized Cauchy type integrals [1]. The method described in this paper is
based on the same principle. However, instead of linking the integral to the complex
potential, as is commonly done, it is linked to the complex velocity. The main
advantages of this approach are: 1) the complex velocity is single-valued and hence
no cuts in the computational domain are necessary and 2) the representing Cauchy
type integral is equivalent to the contour distribution of source and vortex singularities.
By selecting the Cauchy density as the boundary value of a function analytic
in the external flow region, it is possible to specify the far field condition such that
there is no flow in the complementary interior domain. In this particular case the
normal and tangential velocities become decoupled, corresponding to the source
and vortex densities respectively. The imposition of the normal-velocity boundary
condition and the subsequent discretization by boundary elements leads to the
vortex panel method in the complex plane, reported earlier [2].
Keywords
Related Book
Other papers in this volume
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