Sixth Order Accurate Compact Scheme with Group Velocity Control and Application

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.