基于对流项的不同非线性差分格式的稳定性  

The Stability of Different Nonlinear Difference Schemes of Convection Terms

作　　者：胡庆云[1] 王船海[2] 

机构地区：[1]河海大学理学院,江苏南京210098 [2]河海大学水文水资源学院,江苏南京210098

出　　处：《华北水利水电大学学报（自然科学版）》2014年第4期85-92,共8页Journal of North China University of Water Resources and Electric Power：Natural Science Edition

基　　金：河海大学自然科学基金(理科类)(2008431411)

摘　　要：对对流项的处理是水动力学方程计算模拟格式稳定性的关键.针对非线性对流项的不同离散格式,依据稳定性定义,导出误差传播矩阵.通过计算得到稳定域和增长系数,描绘出稳定性图像.稳定域越大、增长系数越小,差分格式的稳定性就越好.据此对常见的差分格式进行稳定性分析、比较和判别.指出初边值条件对稳定性有影响,且边值条件的变化越激烈,稳定性越差.计算的总时长对稳定性也有影响.The calculation of convection terms is the key to the stability of computational simulation format of the hydrodynamic model.The error propagation matrix is derived from different discretization schemes of nonlinear convection terms according to the stability definition. The stability region and the growth factor are calculated and the figure of stability is drawn. If the stability region is bigger and its growth factor is smaller,the difference schemes have better stability. Then the stabilities of some usual difference schemes are analyzed,compared and discriminated. It is found that the initial boundary conditions will influence the stability,and the boundary condition changes more intensively,is worse the stability. The total calculation duration also affects the stability.

关 键 词：误差传播矩阵 稳定域 增长系数 稳定性判别 

分 类 号：O241.82[理学—计算数学]