非线性San Venant方程组数值稳定性分析  

NUMERICAL STABILITY ANALYSIS OF NON-LINEAR SAN VENANT EQUATIONS

作　　者：吴作平 

机构地区：[1]五凌电力有限公司,长沙410004

出　　处：《动力学与控制学报》2010年第3期224-228,共5页Journal of Dynamics and Control

基　　金：国家自然科学基金重大项目资助课题(50099620)~~

摘　　要：分析了非线性San Venant方程组的解的特性,并在统一考虑阻力项的影响的基础上,分析了用Pressmainn格式求解非线性San Venant方程组的数值稳定性和收敛性.研究了φ和θ不同取值情况下,差分方程数值解的收敛情况与相对时间步长(Δt)/(Δx)和相对波长L/(Δx)的关系.指出数值解总是存在衰减和弥散现象,在实际模拟过程中,应合理选择φ和θ值,以兼顾数值衰减幅度和模拟速度.The characteristics of non-linear San Venant equation solutions and their stability and astringency with Preissmainn format considering the influence of resistance were analyzed,and then relations between numerical solution astringency and Δt/Δs and L/Δx in different φ and θ was also discussed. At the end, it＇s pointed out that attenuation and dispersion were always exist, and it＇s important to choose appropriate φ and θ in order to control numerical solutions＇ dispersing range and modeling velocity in actual model.

关 键 词：非线性 稳定性 收敛性 

分 类 号：O175.13[理学—数学]