浅水方程初边值问题几种新的差分格式及其数值试验

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名

邮箱

手机号码

标题

留言内容

验证码

Several New Types of Finite-Difference Schemes for Shallow-Water Equation with Initial-Boundary Value and Their Numerical Experiment

摘要: 本文提出几种有限差分法求解绝对坐标系中浅水方程的新方法;对五个对角线矩阵也提出了效率高而且简单的两级迭代计算的有效方法.这种迭代法可以用来处理浅水方法的多格计算.最后我们研究了初始边界值问题.通过数值试验证明,线性正弦波会逐步变为非线性的圆锥型波.

Abstract: This paper proposed several new types of finite-difference methods for the shallow water equation in absolute coordinate system and put forward an effective two-step predictor-corrector method, a compact and iterative algorithm for five diagonal matrix. Then the iterative method was used for a multi-grid procedure for shallow water equation. At last, an initial-boundary value problem was considered, and the numerical results show that the linear sinusoidal wave would successively evolve into conoidal wave.

[1]	Chu,C.K.,L.W.Xiang & Y.Barasky,Solitary waves induced by boundary motion,Comm.Pure & Appl.Math.,36(1983),495-504.
[2]	Zabusky,N.J.& M.D.Kruskal,Interaction of "soliton" in a collisionless plasma and the recurrence of initial states,Phys.Rev.Lett.,15(1965),240-243.
[3]	Greig,I.S.& J.L.Morris,A hopscotch method for the Kortewey-de Vries equation.J.Comp.Phys.,20(1976),64-80.
[4]	Canosa,J.& J.Gazdag,The Kortewey-de Vries-Burger's equation,J.Comp.Phys.,23(1977),393-403.
[5]	Mei,C.C.,The Applied Dynamics of Ocean Surface Waves,New York,Willy(1983).
[6]	Funk,E.K.,Laboratory research in support of coastal and offshore engineering,Proc.Offshore China(1985).
[7]	Kuo,Pen-yu,A survey of numerical method for solitary waves(Ⅰ),J.Mathematical Research & Exposition 5,2,April(1985)(in Chinese)
[8]	Hackbush,W.,A Lecture Notes on Multi-grid Method,In Xi'an Summer School,China(1985).
[9]	Roache,P.J.,Computational Fluid Mechanics,Hermosa Publishing,Albuquaque(1972).
[10]	周钢,K,d,V.方程的几种差分近似,上海科技大学情报室.