摘要
本文构造了非均匀网格上求解定常对流扩散反应方程的高精度紧致差分格式。我们首先基于非均匀网格上函数的泰勒级数展开,给出了一阶导数和二阶导数的高阶近似表达式;然后将模型方程变形,借助于对流扩散方程高精度紧致格式构造的方法,结合原模型方程,得到定常对流扩散反应方程的高精度紧致差分格式;最后给出的数值算例验证了本文格式高精度和高分辨率的优点。
A high accuracy compact finite difference scheme on the non-uniform grid is proposed to solve the convection-diffusion-reaction equation. Based on the Taylor series expansion, we first constructed the approximate expressions for the lst-order and 2nd-order derivative; then, by rewriting the model equation in the form of the convection diffusion equation and utilizing the model equation, we get the finite difference scheme and illustrate by four numerical examples. The numerical results show that the presented scheme has many advantages such as yielding more accurate numerical solutions, having high resolution for the large gradient changes of the unknown quantity, being suitable for both convection-dominant flows and diffusion-dominant flows and so on.
出处
《工程数学学报》
CSCD
北大核心
2009年第2期219-225,共7页
Chinese Journal of Engineering Mathematics
基金
国家自然科学基金(10662006
10502026)
2008年宁夏高等学校科学技术研究项目
关键词
对流扩散反应方程
高精度紧致差分格式
非均匀网格
对流占优
边界层
convection diffusion reaction equation
high accuracy compact scheme
non-uniform grid
convection domain
boundary layer
