对流扩散反应方程基于坐标变换的高阶紧致差分格式

全文下载：2014010100

兰斌， 薛文强， 葛永斌*

(宁夏大学 数学计算机学院，宁夏 银川 750021)

 摘要： 基于非均匀网格，提出了一种求解一维定常对流扩散反应方程的高精度紧致差分格式。首先采用坐标变换方法将原方程由物理空间的非均匀网格转换为计算空间的均匀网格，然后给出一阶导数和二阶导数在均匀网格上的中心差分逼近式，并结合变换后的方程，得到了定常对流扩散反应方程具有四阶精度的紧致差分格式。 最后，通过数值算例验证了该方法的精确性和高分辨率的特点。数值实验结果表明，对于所研究问题，该方法较不进行坐标变换而直接在物理域上建立的非均匀网格上的高阶紧致格式具有更高精度。

关键词： 对流扩散反应方程； 非均匀网格； 坐标变换； 高阶紧致差分格式

中图分类号： O 241.82文献标志码： A

 A Highorder Compact Difference Scheme Based on the Coordinate

Transformation for the Convection Diffusion Reaction Equation

 LAN Bin，  XUE Wenqiang，  GE Yongbin

 (School of Mathematics and Computer Science, Ningxia University, Yinchuan 750021, China)

 Abstract: A high accurate compact finite difference scheme based on the nonuniform grid is proposed to solve the one dimensional (1D) convection diffusion reaction equation. First, the original equation is transformed from the nonuniform grid of  the physical space to the uniform grid of the computational space by using the coordinate transformation method; then the central difference approximate expressions for the 1storder and 2ndorder derivatives are constructed on the uniform grids. After that, a fourthorder compact difference scheme for the 1D convection diffusion reaction equation is got by using the original equation. At last, the numerical experiments are conducted to show the high accuracy and high resolution of the present method. And the computed results show that the present scheme is more accurate than the highorder compact transformationfree method on the nonuniform grids.

Key words: convection diffusion reaction equation; nonuniform grid; coordinate transformation; highorder compact difference scheme

收稿日期： 20130313

基金项目：国家自然科学基金项目(11061025)；霍英东教育基金会高等院校青年教师基金项目(121105)；宁夏自然科学基金项目(NZ12123)；宁夏大学自然科学基金项目(ZR1120).

作者简介：兰斌(1986—)，男，硕士研究生.*通信联系人.