Convergence of Panel Methods Using Discrete Vortices around Two-Dimensional Bodies

概要

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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 and recently has been applied to complicated body shapes together with the vortex method. In the present paper we demonstrate the mathematical analysis of two panel methods for inviscid incompressible flow past two-dimensional bluff bodies, the pointwise and piecewise-linear distributions of vortices. The governing singular integral equation is derived by distributing vortices on the surface of the body and the simultaneous linear algebraic equations are derived by approximating the integral equation by the discretization of vorticity distribution. The analytic solution of the linear algebraic equations is obtained and the accuracy of the approximate solution is discussed. We show that : (1) there 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 equation cannot be obtained using these schemes unless they are modified.
一般社団法人日本機械学会の論文
1996-11-15