捕捉激波的群速度控制方法

摘要

The basic principles and the recent developments of group velocity control (GVC)method are reviewed.GVC method is a new shock capture method by controlling the dispersion error of numerical schemes.In GVC method,the “fast”scheme is used in front of the shock and the “slow”one is used behind the shock,and in this way,the spread of numerical oscillations is limited in a very small region near the shock,and thus the oscillations are suppressed.The GVC method capture shock mainly by using dispersion technique,therefore,the dissipation of GVC schemes is relatively low.The recently developments of GVC schemes,such as compact GVC scheme,optimized GVC scheme,hybrid weighted GVC-WENO scheme and GVC scheme by group velocity booster,are also reviewed.GVC schemes are useful methods for detail simu-lation of multi-scale flows.%回顾及综述了群速度控制方法基本原理、发展过程及最新进展。群速度控制方法是通过控制色散误差以捕捉间断的一种数值方法。该方法通过在间断两侧采用不同色散类型的格式，将数值波的传播压制在间断附近，避免数值振荡向周围扩散，从而达到抑制数值振荡的效果。该方法主体上采用数值色散抑制振荡，实际使用中仅需补充较低水平的数值耗散就可将振荡压制在可接受的范围内。因而群速度控制格式的总体耗散水平较低，易于实现小尺度波的高分辨率捕捉，是复杂流动高分辨率数值模拟的有效方法。