高维三次样条插值法在气动参数计算中的应用

根据一维三次样条插值算法能够达到二阶连续的光滑程度，将其扩展到高维插值，应用到由多自变量决定的气动参数计算。相对于高维线性插值算法，提高了插值精度，同时又避免了高次拉格朗日插值中的失真现象。并针对于高维三次样条插值算法，提出一种改进的边界条件，能够提高插值精度，简便工程应用。通过标准函数的数值试验，证明该高维插值方法及其改进边界条件对气动参数计算精度的提高是明显的。

Application of High-dimensional Cubic Spline Interpolation Method in the Calculation of the Aerodynamic Parameters

One-dimensional cubic spline interpolation algorithm with second-order continuous smooth degree is extended to a high-dimensional interpolation which can be applied to the calculation of aerodynamic parameters determined by a number of independent variables. Compared to the high-dimensional linear interpolation algorithm, it improves the interpolation accuracy, while avoiding the distortion cause by the high-Lagrange interpolation. Improved boundary condition, which can improve the interpolation accuracy and simplify engineering applications, is proposed. The obvious improvement of accuracy is demonstrated by the result of numerical experiments