基于自适应小波配点法的水击数值计算
许志宇1,2,谭永华2,3,李小明1

(1.西安航天动力研究所,陕西 西安 710100;2.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)

水击; 自适应小波配点法; 数值计算

Numerical computation of water-hammer based on adaptive wavelet collocation method
XU Zhiyu1,2, TAN Yonghua2,3, LI Xiaoming1

(1.Xi'an Aerospace Propulsion Institute, Xi'an 710100, China; 2.Science and Technology on Liquid Rocket Engine Laboratory, Xi'an 710100, China; 3.Academy of Aerospace Propulsion Technology, Xi'an 710100, China)

water-hammer; AWCM; numerical computation

备注

为了克服传统谱方法计算水击问题的数值振荡,选择具有紧支撑特性的样条小波代替传统的基函数,建立了一维流体运动方程的自适应小波配点计算格式,并对有摩擦和无摩擦的一维管路水击问题进行了数值计算,获得了水击波的传播过程。结果 表明:小波配点法能够准确计算水击波的传播过程,在水击波波阵面处,不会因高分辨率出现剧烈的数值振荡现象,精度和分辨率可以同时提高; 自适应算法能够自动捕捉水击波位置,并在水击波局部区域采用高分辨率计算,而在梯度较小区域降低分辨率计算,在保障精度和分辨率的前提下,显著节约计算量。

In order to restrain the numerical oscillation of computing water-hammer problem using the traditional spectral method, an Adaptive Wavelet Collocation Method(AWCM)based on the compactly supported spline wavelet was established for the one-dimensional fluid motion equation.The water-hammer problems of one-dimensional pipeline with friction and without friction were numerically computed, and the propagation process of water-hammer wave was obtained.The results show that the Adaptive Wavelet Collocation Method can accurately compute the propagating process of water-hammer wave.At the wavefront, there will be no sharp numerical oscillation phenomenon due to the high resolution, and both the accuracy and resolution can be improved simultaneously.In addition, the method can automatically capture the position of water-hammer wave, and adopt the high resolution in the local area of water-hammer wave while reduce the resolution in the small gradient area, which save the computational cost largely on the premise of guaranteeing the accuracy and resolution.