冲击波的小波数值计算方法  

Numerical computation of shock wave using wavelet methods

作　　者：许志宇[1,2] 谭永华 李小明 XU Zhiyu;TAN Yonghua;LI Xiaoming(Xi’an Aerospace Propulsion Institute,Xi’an 710100,Shaanxi,China;Science and Technology on Liquid Rocket Engine Laboratory,Xi’an Aerospace Propulsion Institute,Xi’an 710100,Shaanxi,China;Academy of Aerospace Propulsion Technology,Xi’an 710100,Shaanxi,China)

机构地区：[1]西安航天动力研究所,陕西西安710100 [2]西安航天动力研究所液体火箭发动机技术重点实验室,陕西西安710100 [3]航天推进技术研究院,陕西西安710100

出　　处：《爆炸与冲击》2020年第1期80-88,共9页Explosion and Shock Waves

摘　　要：基于自适应小波配点法和人工黏性技术,构造出一种简单稳定的冲击波数值计算方法。采用小波阈值滤波,生成适应流场分布的多尺度自适应网格,并利用密度场最细尺度的小波系数构造幂函数形式的冲击波定位函数,用以判断冲击波位置。联合人工黏性与冲击波定位函数,自动根据流场梯度严格控制人工黏性的大小和分布。对强/弱冲击波管问题进行计算,结果表明,该方法能够准确捕捉冲击波和有效抑制数值振荡,并且使用简单、分辨率高、计算量小。A simple and stable wavelet method, which is based on adaptive wavelet collocation methods and artificial viscosity techniques, was proposed to compute shock waves. Dynamic multiscale grids generated by wavelet threshold filtering adaptive to the flow field were used. The shock waves can be checked out by the shock locator functions with power formula,which are constructed through using the magnitudes of the wavelet coefficients on the finest level in the density fields. Then,the artificial viscous terms including viscosity and shock locator functions strictly control the magnitudes and distributions of the artificial viscosity according to the gradients in the flow field. A strong and a weak shock tubes were computed, which shows that the method can accurately capture shock fronts and effectively restrain numerical oscillations. By the way, it is easy to manipulate, high of resolution and small of computational costs.

关 键 词：冲击波 自适应小波配点法 数值振荡 人工黏性 

分 类 号：O354.5[理学—流体力学]