关键词: 迎风紧致格式, Fourier分析, 色散关系, 群速度

Abstract: Based on the Fourier analysis method, a fully-discretized dispersion relation is derived for a family of high accuracy upwind compact difference schemes by considering one dimensional linear convetion equation temporally discretized by the explicit multi-step Runge-Kutta algorithm. The effects of CFL numbers on the characteristics of these schemes, including dissipation and dispersion errors, phase velocity and group velocity, are analyzed. The two-dimensional anisotropy problem is discussed. Moreover, an eigenvalue analysis is performed. Two numerical examples are used to show the high accuracy and resolution of these schemes.

Key words: upwind compact difference scheme, Fourier analysis, dispersion relation, group velocity