带间断非线性定常对流扩散方程的高精度解法  

A High-order Accuracy Method for Solving Nonlinear Convection Diffusion Equations with Discontinuity

作　　者：陈雪钦 王晓峰 晏云 CHEN Xueqin;WANG Xiaofeng;YAN Yun(School of Biological Science and Biotechnology,Minnan Normal University,Zhangzhou Fujian 363000,China;School of Mathematics and Statistics,Minnan Normal University,Zhangzhou Fujian 363000,China)

机构地区：[1]闽南师范大学生物科学与技术学院,福建漳州363000 [2]闽南师范大学数学与统计学院,福建漳州363000

出　　处：《莆田学院学报》2024年第5期33-38,共6页Journal of putian University

基　　金：福建省自然科学基金面上项目(2022J01897);福建省中青年教师教育科研项目(JAT200295)。

摘　　要：针对一类带有间断系数的非线性定常对流扩散方程,提出了一种高精度的紧致有限差分方法;该方法在内点处采用的是三点四阶的差分格式,在边界点与间断点处采用的是两点三阶的差分格式;给出的数值算例表明这种新的方法整体求解精度可以达到四阶。A high-order accuracy compact finite difference method was developed to solve nonlinear steady-state convection diffusion equations with discontinuous coefficients.Three-point fourth-order accurate difference schemes were used for the inner points,and two-point third-order accurate difference schemes were applied to the boundary points and discontinuous point.Numerical example shows that the present new method can reach fourth-order accuracy globally.

关 键 词：非线性对流项 对流扩散方程 高精度 间断 定常 有限差分 

分 类 号：O241.7[理学—计算数学] O241.8[理学—数学]