无网格方法关于导数计算的程序验证  

Code verification of mesh free method with computation of derivatives

作　　者：马智博[1] 赵亚洲[2] 

机构地区：[1]北京应用物理与计算数学研究所,北京100094 [2]中国科学院地质与地球物理研究所,北京100029

出　　处：《航空动力学报》2017年第8期1886-1899,共14页Journal of Aerospace Power

基　　金：国家自然科学基金(11371066)

摘　　要：为了提高无网格方法对空间导数的数值计算能力,提出并论证了新的适用于直角坐标系、柱坐标系和球坐标系的空间导数无网格算法。基于数值解与理论解的对比分析,对数值误差和收敛性进行了后验评估。评估结果表明:该算法对函数和导数的估计均为2阶精度,支撑域尺度对数值误差的大小有一定影响,但不影响数值计算的精度等级。在离散尺度h为0.01的条件下,对所选函数及其导数的数值计算相对误差不大于0.65%。In order to improve the approximation of spatial derivatives without meshes,a set of mesh free method for spatial derivatives was developed,which agreed well with the Cartesian,cylindrical and spherical coordinates.Based on the comparisons between numerical and theoretical solutions,the errors and convergences were assessed by a posteriori method,showing that the approximations for functions and derivatives were of the second order accurate,and the scale of the support domain had some influences on numerical errors but not on accuracy orders.With a discrete scale h being 0.01,the relative errors of the numerical simulation for the selected functions and their derivatives were within 0.65 %.

关 键 词：无网格方法 光滑粒子法 物理质团法 空间导数近似计算 验证与确认 

分 类 号：V23[航空宇航科学与技术—航空宇航推进理论与工程] O242.1[理学—计算数学]