Note on Governing Equations for a Discrete Vortex Method

Abstract

This note investigates the characteristic of a coefficient matrix, which is derived from governing equations used in a discrete vortex method. When singular points on a body are arranged symmetrically, the rank of the coefficient matrix is reduced. Namely, the matrix is singular. When Kelvin's theorem is introduced in order to avoid the reduction of rank, that becomes regular. Then, governing equations can be solved by using a suitable method. When those are arranged asymmetrically, another unknown parameter should be introduced.