计算函数导数的FODF-SPH方法

发布时间：2018-06-03 02:56

  本文选题：SPH核近似方法 + FODF-SPH方法　； 参考：《数学的实践与认识》2016年13期

【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.
[Abstract]:Based on the principle of smooth particle hydrodynamics and the kernel approximation method of smooth Particle hydrodynamics, a new FODF-SPH(Frist Order Derivative free: FODF method for calculating the derivative of function is proposed by Taylor series expansion, and the one-dimensional, two-dimensional and three-dimensional cases are derived, respectively. The discrete form of the derivative kernel estimation of a function is calculated. The derivatives of one-dimensional and two-dimensional functions are calculated by using different particle spacing and different smooth length, and the error is compared with the traditional SPH method. The results show that compared with the traditional method, the proposed method has the advantages of small error, fast convergence and avoiding the calculation of the derivative of kernel function, so it has a strong scope of application in engineering application and numerical calculation.
【作者单位】： 新疆大学数学与系统科学学院;
【基金】：国家自然科学基金(51565054,51075346)
【分类号】：O35
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本文编号：1971193