非线性对流扩散方程的预报校正紧差分格式  

A predictor-corrector compact finite difference scheme for the nonlinear convection diffusion equation

作　　者：杨录峰[1] 

机构地区：[1]北方民族大学信息与计算科学学院,银川750021

出　　处：《黑龙江大学自然科学学报》2013年第4期462-465,470,共5页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(10961002);北方民族大学自主科研项目(2011ZQY026)

摘　　要：结合预报校正的MacComack方法与高阶紧致差分格式方法的优点,在空间导数采用四阶紧致差分格式进行离散之后,对得到的空间半离散格式采用预报校正的MacCormack方法进行时间推进,得到一种求解非线性对流扩散方程的高精度方法。数值试验表明,该格式可以有效求解非线性对流扩散方程,显示出算法的有效性。A new high-order compact scheme is proposed for the nonlinear convection diffusion equation, which is combined with predictor-corrector MacCormack method and high-order compact schemes. The spatial derivatives are discretized by fourth-order compact finite scheme, and the spatial semi-diseretized equations is solved by a predic- tor-corrector MacCormaek method in time. Numerical experiments show that the nonlinear convection diffusion e- quation can be effectively solved by the new high-order compact scheme. The effectiveness of the proposed method is verified by experiments.

关 键 词：紧致差分格式 预报校正 MacCormack方法 非线性对流扩散方程 

分 类 号：O241.82[理学—计算数学]