涡格法中Multhopp离散的超收敛性的进一步研究

在中弧线为四阶以下多项式的二维薄翼绕流问题的研究中，Ｍｕｌｔｈｏｐｐ离散超收敛性的证明展示了涡格法中优化的离散化格式的潜力。本文把这一研究扩展到中弧线为任意Ｎ阶多项式的二维薄翼绕流的一般情况。通过误差分析，证明了Ｍｕｌｔｈｏｐｐ离散对该问题可以得到离散化误差为零的翼面涡密度、升力和俯仰力矩，唯一的要求是使用的离散元数目应大于［（Ｎ＋１）／２］。

A Further Study on the Superconvergence of Multhopp's Discretization in Vortex-Lattice Methods

An earlier proof of the superconvergence of Multhopp's discretization for the flow past a two-dimensional thin airfoil, with camber line represented by a polynomial of degree up to 4, showed the potentiality of an optimal discretization scheme for vortex-lattice methods. In the present paper, the study of the superconvergence of Multhopp's discretization is extended to the more general flow past a thin airfoil, with camberline represented by a polynomial of arbitray degree N. The approach is based on an error analysis. We show that the numerical solution for the vorticity density on the camber line is in complete agreement with the exact solution when a Multhopp's discretization is used, the lift and pitching moment are also exact.To obtain this kind of high accuracy, the only limitation is that the number of the clements used is greater than (N 1) /2]