中文摘要：

在光滑粒子流体动力学（Smooth Particle Hydrodynamics：SPH）核近似方法原理的基础上,通过泰勒级数展开提出了计算函数导数的新FODF-SPH（Frist Order Derivative Free：FODF）方法,并分别推导一维、二维及三维情况下,计算函数的导数核估计的离散形式.用不同的粒子间距和不同的光滑长度计算一维和二维函数导数,与传统SPH方法进行误差对比分析.结果表明,与传统方法对比提出的计算方法的误差小、收敛速度快且计算过程避免核函数导数计算等优越性,因此在工程应用和数值计算中具有较强的适用范围。

英文摘要：

Based on the basic principle of the smooth particle hydrodynamics （SPH） method＇s kernel approximation, New FODF-SPH （Frist Order Derivative Free Smoothed Particle Hydrodynamics） method to compute first order derivatives are constructed through Taylor series expansion. The Discrete forms of kernel estimations are deduced in the one, two and three dimensional space. Then selecting different particle distance and setting different smooth length computed one and two dimensional function＇s derivatives, compared and an- alyzed errors of traditional SPH method and FODF-SPH methods. The results show that error of new methods is relatively smaller and convergence speed is faster than traditional SPH method; also in calculation process can avoid calculation of kernel function＇s derivative kernel approximation, so this method have a wider range of application in engineering an numerical calculation.