基于人工黏性的二维激波小波多尺度数值计算

Multiscale Numerical Computation of Two-Dimensional Shock Waves Based on Wavelet Methods and Artificial Viscosity

关键词:  激波  自适应小波配点法  数值振荡  激波定位函数  人工黏性

Key words:  Shock wave  Adaptive wavelet collocation method  Numerical oscillation  Shock locator function  Artificial viscosity

摘要:

基于自适应小波配点法和人工黏性，构造了二维激波问题的小波数值计算格式。利用最细尺度的小波系数构造两组激波定位函数，分别用以控制两个正交方向（x，y方向）人工黏性的大小和分布，对三类二维激波问题进行计算和验证。结果表明：自适应小波配点法利用小波阈值滤波删除变化平缓区域大量网格点，而保留变化急剧区域的网格点，比传统方法计算效率高，且分辨率越高，计算效率更高；利用最细层小波系数构建的幂函数形式的激波定位函数能准确判断激波位置和控制x，y方向人工黏性的大小和分布，从而捕捉不同方向和不同强度的激波。

Abstract:

A simple and steady wavelet numerical method based on adaptive wavelet collocation method and artificial viscosity was constructed for two-dimensional shock wave problems. The method utilizes the wavelet coefficients of the density fields on the finest level to generate a pair of shock locator functions in x and y directions， in order to control artificial viscosity domains and magnitudes. Finally， three classical shock problems were computed to demonstrate how the method works and its features. Results show that the adaptive wavelet collocation method is more efficient than non-adaptive methods， for a large number of collocations in smooth domains are deleted and only a small part are remained through wavelet threshold filtering， and it turns more and more efficient for higher resolutions. For two-dimensional cases， the method can accurately capture shock waves of different directions and strength， through adding artificial viscosity depending on the shock locator functions that are constructed by wavelet coefficients on the finest levels in x and y directions.