Modified method of regularized sources for potential flow

Abstract

This paper describes the development of the Method of Regularized Sources for potential flow problems. It is based on the modification of the fundamental solution near the source point by replacing the singularity with a blob in form of a steep rational function. This allows to solve the problems in the same way as with Method of Fundamental Solutions, however without an artificial boundary. Method of Regularized Sources gives excellent results for Dirichlet boundary conditions, however it fails for Neumann boundary conditions. To overcome this problem are the source point positions on the segments of the boundary with Neumann boundary positions placed close to the collocation points. This approach somehow represents a blending of the Method of Regularized Sources and the classical Method of Fundamental Solutions. The novel approach is characterized by two free parameters; the blob thickness and the artificial boundary displacement position. A two-dimensional numerical example of potential flow around circle is analyzed in detail regarding these two free parameters. The modified Method of Regularized Sources gives even more accurate results for potential and derivatives than the Method of Fundamental Solutions. The source point can be placed 2–25 times closer to the boundary collocation points than with the classical Method of Fundamental Solutions and thus reduces the problem of the placement of the artificial boundary.