六阶精度的群速度直接控制紧致格式及其应用

Sixth Order Accurate Compact Scheme with Group Velocity Control and Application

差分数值解产生非物理振荡的直接原因是在于非均一的波群的群速度,因此本文利用直接群速度控制的方法重新构造具有六阶精度的紧致型差分格式,以达到改善激波数值解的目的。对所构造的格式的精度及数值解随控制参数变化的行为进行了分析。最后文中给出了一些典型算例,证明了文中所构造的格式具有方法简便,物理含义清楚,精度高,网格基架点小,和捕捉激波能力较强的优点。

The direct reason of nonphysical oscillations in numerical solution is the non-uniform group velocity. This essay developed a modified sixth order accurate compact scheme with the method of group velocity control, and analyzed its accuracy and the behavior of numerical solution with Taylor method and Fourier method. The scheme is high order accurate with less stencil, simple, clear in physical explaining, and efficient in shock capturing. At last, some numerical experiments show the efficiency of the method.