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A Voronoi Cells Based C~∞ Interpolation Basis Function and Its Application in CFD

ZHU Huaiqiu\ WU Jianghang (State Key Laboratory for Turbulence Research,Department of Mechanics and Engineering Science,Peking University,Beijing,100871)  
According to the ideal of Natural Neighbor Interpolation,based on the geometric characteristics of Voronoi cells,this paper describes a C ∞ interpolation basis function,which is smooth and continuously differentiable everywhere except at its defining node.The parametric expression of first derivatives of the interpolation basis function is also given.The new theory for function and derivative interpolation has application in CFD to develop a novel Finite Element Method (FEM) which is called Natural Element Method (NEM).In addition,it demonstrates that the C ∞ interpolation basis function can be the promising role in a range of visualization problems of CFD.
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