摘要
本文把三层修正特征线法,MMOCAA 差分方法及WENO 插值相结合,提出了求解对流扩散方程的三层WENO-MMOCAA 差分格式.此格式关于时间具有二阶精度,关于空间具有二阶以上精度且可避免基于二次以上Lagrange 插值的三层MMOCAA 差分方法在解的大梯度附近所产生的振荡.本文使用新的分析方法,给出了格式的误差估计.本文的数值算例表明新格式可消除振荡.
Combing the three-step modified method of characteristics, MMOCAA difference method with WENO interplation, the three-step WENO-MMOCAA finite difference method is established for convectiondominated diffusion problem in the paper. The scheme is two-order accurate in time and more than two-order accurate in space. The scheme is free from the oscillation near the steep front, with which the problem is solved by three-step MMOCAA finite difference method based on m-order （m ≥ 2） Lagrange interplation. Using the new analysis method, we give the estimate analysis of the scheme. The numerical example show that the new scheme can erase the oscillation.
出处
《应用数学学报》
CSCD
北大核心
2005年第4期713-722,共10页
Acta Mathematicae Applicatae Sinica
基金
南开大学科技创新基金(05-06号)资助项目.
关键词
对流占优扩散方程
三层修正特征线法
MMOCAA差分方法
WENO插值
convection-dominated diffusion problem
the three-step modified method of ch^razteristics
MMOCAA finite difference method
WENO interplation
