不同核函数对光滑粒子流体动力学计算结果的影响分析  

Analysis of Calculation Results of Different Kernel Functions on the Smooth Particle Hydrodynamics

作　　者：王平[1] 王亮 魏承印 吴杰 孔为 WANG Ping;WANG Liang;WEI Chen-ying;WU Jie;KONG Wei(School of Mathematics and Information Engineering,Lianyungang Normal College,Lianyungang 222006,China;School of Energy and Power,Jiangsu University of Science land Technology,Zhenjiang Jiangsu 212003,China)

机构地区：[1]连云港师范高等专科学校数学与信息工程学院,江苏连云港222006 [2]江苏科技大学能源与动力学院,江苏镇江212003

出　　处：《数学的实践与认识》2020年第11期218-226,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金(21406095)。

摘　　要：分别基于β-样条、新四次函数及五次样条三类光滑核函数,利用光滑粒子流体动力学方法,计算分析典型方腔剪切流和泊肃叶流动.通过对运动粒子空间分布、流动流速特性等分析,研究了不同光滑核函数对计算结果的影响.结果认为:基于β-样条及五次样条核函数的光滑粒子流体动力学计算结果标准误差分别为1.02×10^-4和1.54×10^-4,能恰当的反应流体的流动状态,但基于五次样条核函数的计算结果易导致粒子分布的不均匀性,破坏计算的稳定性.而新四次核函数的计算结果精度及运算效率较低,与流体的流动特性存在较大差异.研究结果可为提高光滑粒子流体动力学的计算精度提供重要参考.The shear flow and the Poiseuille flow are studied by using the smooth particle hydrodynamics,which is based on the kernel function ofβ-spline,new quartic and quintic spline,respectively.The spatial distribution of particle and the flow velocity characteristics are analyzed,and it is used to study the calculation results of different kernel functions on the smooth particle hydrodynamics.The result shows that the calculation accuracy ofβ-spline kernel function is highest.For the kernel function ofβ-spline and quintic spline,the flow state can be calculated accurately,and the standard error of the calculation result is 1.02×10^-4 and 1.54×10^-4,respectively.But the inhomogeneity of particle distribution is easy caused by the quintic spline kernel function,and the stability of calculation will be poorly.However,for the new quartic kernel function,the calculation accuracy and the operation efficiency is lowest,and it is cannot accurately express the flow state.These results are important for improve the calculation accuracy of smooth particle hydrodynamics.

关 键 词：光滑粒子流体动力学 不同核函数 计算精度 

分 类 号：O35[理学—流体力学]