サブパネルを用いた内部ディリクレ形式のパネル法について

抄録

A panel code using subpanel technique, based on the internal Dirichlet formulation has been developed. In this study, only the case where the internal region has no flow is considered. Every panel is devided into 9 flat subpanels. Each subpanel has 4 subgrid points which are located on the biquadratic curve defined between two neibouring grid points, which effects more accurate expression of the geometry. Each subpanel is assumed to have uniform density of singularity, the value of which is expressed at the center of the subpanel using two-dimensional quadratic interpolation functions defined with the geometry of the surrounding panels. The calculated results are compared with those obtained by the panel method based on the external Neumann formulation using the same subpanel technique. Both results show good agreements in external flow examples, but in the calculation of the flow suffering strong interaction such as a flow through a duct, the panel code of the internal Dirichlet formulation gives much better results than that of the external Neumann formulation. This suggests that the internal Dirichlet panel method could be applied more effectively to the problems, such as wings with wing-tip clearance or wing-tip vortex sheet, which have severe interactions with the nearby singularity surfaces.