基于迎风LDQ方法解Burgers方程  

The LDQ method with upwind scheme for solving Burgers equations

作　　者：陈龙 张学莹[1] 胡婷婷[2] 

机构地区：[1]河海大学理学院,江苏南京210098 [2]华中师范大学数学与统计学院,湖北武汉430079

出　　处：《西北师范大学学报（自然科学版）》2017年第6期10-15,21,共7页Journal of Northwest Normal University(Natural Science)

基　　金：教育部留学回国人员科研启动基金资助项目(20145003412);江苏省自然科学基金资助项目(BK20160853)

摘　　要：以RBF作为LDQ方法的基函数,建立具有迎风格式的LDQ方法,将此方法用在解Burgers方程上,并与传统的无网格方法比较.该方法先要建立一个局部支撑域,在处理对流项离散时选用该局部支撑域,而在处理扩散项离散时根据流动速度的移动方向来选择局部支撑域,然后建立局部线性方程组,再推广成全局形式,以获得方程组的近似解.实验结果表明该方法具有较高的数值精度.The differential quadrature method based on radial basis function with upwind scheme isproposed for solving the Burgers equations, and its numerical performance is compared with traditionalLDQ method. Firstly a local support domain is created, and the diffusion term is the original support domain, while the convection term is discretized by shifting the support domainaccording to the stream line direction. The discrete nodes of the support domain are used to construct a low order linear system for obtaining the coefficients of equations, then extended to global for obtain the approximate solutions for the Burgers equation. Numerical results show the methods have higher accuracy for solving the Burgers equations.

关 键 词：无网格方法 径向基函数 迎风格式 BURGERS方程 局部支撑域 

分 类 号：O241.82[理学—计算数学]