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通常的粘性项处理方法是连续两次采用结点型中心差分格式求得。但是,通过两次采用高阶结点型中心格式求得的粘性项易在流场中的“间断”附近产生数值振荡。本文采用多种格式,通过求解一维Burgers方程来充分展示了这种振荡现象。为了消除这种数值振荡,一种半结点型的高阶紧致格式被用来求解粘性项。Fourier频谱分析表明,这种格式具有非常优越的保频谱性能。一维和二维的数值计算结果表明,通过“半结点-结点”交错采用这种半结点型格式的方法可以非常有效地避免粘性项高阶离散可能导致的数值振荡。
The usual sticky item processing method is to use the knot center differential format twice in succession. However, the viscous term obtained by twice using the higher order node-centered format tends to produce numerical oscillations near the “discontinuity” in the flow field. In this paper, we use a variety of formats to fully demonstrate this oscillation by solving the one-dimensional Burgers equation. In order to eliminate this numerical oscillation, a semi-knot high-order compact scheme is used to solve the sticky term. Fourier spectrum analysis shows that this format has a very superior spectrum preserving performance. One-dimensional and two-dimensional numerical results show that by using the “half-node-node” method, the semi-node scheme can effectively avoid the numerical oscillations that may be caused by the high-order dispersion of viscous terms.