Abstract: 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.

Key words: meshfree SPH method, multiscale reproducing kernel function, multi-resolution analysis, optimal support radius, adaptation guidelines