摘要
摄动有限差分(PFD)方法从一阶迎风差分格式出发,将差分系数展开为网格步长的幂级数,通过提高修正微分方程的逼近精度来获得更高精度的差分格式。由于格式基于一阶迎风格式,因此具有迎风效应、网格节点少等特点。本文首先通过对Burgers方程的摄动差分格式的推导,将摄动有限差分格式引入时间相关法的计算,并构造了守恒形式的摄动有限差分格式,然后推广到一维Navier-Stokes方程组的计算。数值比较研究表明:本文构造的NS方程摄动有限差分格式具有比一阶迎风较高的精度和分辨率,而且保持了一阶迎风格式的无振荡性质。
In the peturbational finite difference （PFD） method, the difference coefficients of the first-order accurate upwind difference scheme are expanded into the power series of grid size, by improving the approach accuracy of modified differential equation to obtain higher-order accurate difference scheme. PFD scheme has upwind effect and only uses three grids as in the first-order upwind difference scheme. In this paper, the PFD scheme of the Burgers equation is derived. Then combined with the time depending method, the conservative-type PFD scheme is constructed and generalized to compute one-dimensional Navier-Stokes equations. The numerical results show that the present PFD scheme of NS equations has higher order accurate and better resolution than the first-order accurate upwind scheme does, and can remain the essentially non-oscillatory property.
出处
《空气动力学学报》
EI
CSCD
北大核心
2006年第3期335-339,共5页
Acta Aerodynamica Sinica
基金
国家自然科学基金(10402043)资助课题
关键词
摄动有限差分格式
NS方程
激波计算
peturbational finite difference scheme
Navier-Stokes equation
shock-wave computing
作者简介
申义庆（1969-），男，副研究员，从事流体力学数值方法及数值模拟研究．
