Desingularised Method Of Double Layer
Fundamental Solutions For Potential
Flow Problems
Author(s)
B. Šarler
Abstract
This paper describes an application of the recently proposed Modified Method of
Fundamental Solutions (MMFS) to potential flow problems. The solution in two
dimensional Cartesian coordinates is represented in terms of the double layer
fundamental solution of the Laplace equation. The collocation is used for
determination of the expansion coefficients. This novel method does not require
a fictitious boundary unlike the conventional Method of Fundamental Solutions
(MFS). The source and collocation points thus coincide on the physical boundary
of the system. The desingularised value of the fundamental solution is in case of
the coincidence of the collocation and source points determined from the
respective integral equations logic. The values of the derivatives of the double
layer fundamental solution in the coordinate directions, as required in potential
flow calculations, are calculated indirectly from the considerations of the
constant potential field. A numerical example of potential flow around the two
dimensional circular region is shown. The results with the MMFS are compared
with the results of the classical single layer MFS with an artificial boundary, and
the analytical solution. It is shown that the MMFS gives better accuracy of the
velocity components as compared with the classical MFS.
Keywords: potential flow, method of fundamental solutions, desingularisation,
double layer potential.
1 Introduction
In recent years there has been strong development in mesh reduction methods
in which the polygon-like meshes are reduced or avoided. The MFS is a
Keywords
potential flow, method of fundamental solutions, desingularisation,
double layer potential.
Related Book
Other papers in this volume
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