一维非定常对流扩散方程非均匀网格上的高阶紧致差分格式  

A High Order Compact Difference Scheme on Non-Uniform Grids for the 1D Unsteady Convection Diffusion Equation

作　　者：赵飞[1] 陈建华[1] 葛永斌[1] 

机构地区：[1]宁夏大学数学计算机学院,宁夏银川750021

出　　处：《西安理工大学学报》2013年第4期475-480,共6页Journal of Xi'an University of Technology

基　　金：国家自然科学基金资助项目(11061025;11361045);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)

摘　　要：针对一维非定常对流扩散方程，在非均匀网格上提出了一种两层高精度紧致差分格式，其时间具有2阶精度，空间具有3～4阶精度；然后采用Fourier分析方法给出格式的稳定性条件。最后通过数值算例验证了本文格式对于求解一维含边界层非定常对流扩散问题具有明显的优势。A two-level high order compact difference scheme on non-uniform grids is proposed for solving the 1 D unsteady convection diffusion equation. The scheme is the second order accuracy for time and the third to the fourth order accurate for space. Then, Fourier analysis method is employed to get the stability condition of the scheme. Finally, numerical experiments are conducted to demonstrate that the present method has obvious advantages for solving the 1 D unsteady convection diffusion problems with boundary layers.

关 键 词：非定常对流扩散方程 非均匀网格 高精度紧致差分格式 边界层 

分 类 号：O241.82[理学—计算数学]