摘要
本文提出差分格式的摄动方法,对二阶指数型格式中对流系数和源项作二阶修正,推演出对流扩散方程的四阶指数型格式。该四阶格式的基本结构与二阶指数型格式完全相同,且其系数或源项中所含二阶修正可根据二阶格式计算结果一次性确定,使得计算十分简便。一至三维的四阶指数型格式均具有无条件稳定性,用于Burgers方程等流体力学模型问题,且与常用格式进行了比较,显示出良好的精度,并能较好地适应大梯度区域。
A kind of exponential finite difference schemes with h4 consistency are developed in this study. The h4 scheme is obtained from a second-order modification of the convective coefficients and the source term in an h2 scheme, and the modification could be determined once and for all from computational information of the h2 scheme, which bring great convenience to the h4 scheme. The proposed exponential scheme are unconditionally stable, and show a excellent accuracy and adaptability to great gradient variation when applicated in illustrative computations of ID to 3D fluid flow model problems.
出处
《计算物理》
CSCD
北大核心
1991年第4期359-372,共14页
Chinese Journal of Computational Physics
关键词
对流扩散方程
差分格式
流体力学
fluid mechanics, convective diffusion equation, exponential finite difference scheme.
