CONVERGENCE OF PANEL METHODS USING DISCRETE VORTICES AROUND 2-DIMENSIONAL BODIES

The panel method in which vorticity is distributed on the surface of a body, the surface vorticity distribution method such like the vortex lattice method, is useful for determining the Euler flow past bodies a nd recently has been applied to complicated body shapes together with the vortex method. In the present paper we demonstrate the mathematica l analysis of two panel methods for inviscid incompressible flow past two-dimensional bluff bodies, the pointwise and piecewise-linear distr ibutions of vortices. The governing singular integral equation is deri ved by distributing vortices on the surface of the body and the simult aneous linear algebraic equations are derived by approximating the int egral equation by the discretization of vorticity distribution. The an alytic solution of the linear algebraic equations is obtained and the accuracy of the approximate solution is discussed. We show that: (1) t here exists an appropriate collocation point. (2) the accuracy of the vortices on the surface of the body is of the order of 1/n where n is the panel number and (3) the eigensolution of the governing integral e quation cannot be obtained using these schemes unless they are modifie d.