SPH核函数光滑长度最优选取和自适应准则研究

基于小波分析理论和RKPM再生核函数研究无网格方法SPH中多尺度诊断工具，多尺度再生核函数使得数值计算在不同尺度上的响应分离，并通过动态伸缩窗函数给出计算域不同位置的时频特性，实现在无网格体系下构造网格计算方法的“自适应网格”，从而达到对不同流场位置多分辨率分析的目的.利用多尺度诊断工具中的小波分解算法给出SPH核函数在频域内能量残差估计，发展一种核函数光滑长度最优选取准则.最后，基于可压缩流场激波稀疏波共存的现象，针对传统的光滑长度自适应的缺陷，构造一种避免数值计算“拖尾”现象的自适应准则.

A Study of Optimal and Adaptive Rule of Smooth Length in SPH Kernel Function

Based on wavelet analysis theory and reproducing kernel function, a multiscale diagnostic tool for meshfree method SPH is developed.Multi-scale reproducing kernel function make it possible to separate numerical computation response at different scales.Frequency characteristics of computational domain at different position is depicted by dynamic retractable window function, which constructs "adaptive mesh" in mesh method for meshfree system to carry multi-resolution analysis at different position of flow field.With wavelet decomposition algorithm in multi-scale diagnostic tool, a kernel smoothing length optimal selection rule is developed on the basis of estimated energy error ratio of SPH kernel function in frequency domain.Finally, for shock/rarefaction wave coexistence in compressible flow field and defects of traditional method, we construct a numerical method to avoid "tailing" phenomenon.