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浅水方程初边值问题几种新的差分格式及其数值试验

吕秋强 周钢 刘应中

吕秋强, 周钢, 刘应中. 浅水方程初边值问题几种新的差分格式及其数值试验[J]. 应用数学和力学, 1989, 10(3): 259-269.
引用本文: 吕秋强, 周钢, 刘应中. 浅水方程初边值问题几种新的差分格式及其数值试验[J]. 应用数学和力学, 1989, 10(3): 259-269.
Lü Qiu-qiang, Zhou Gang, Liu Ying-zhong. Several New Types of Finite-Difference Schemes for Shallow-Water Equation with Initial-Boundary Value and Their Numerical Experiment[J]. Applied Mathematics and Mechanics, 1989, 10(3): 259-269.
Citation: Lü Qiu-qiang, Zhou Gang, Liu Ying-zhong. Several New Types of Finite-Difference Schemes for Shallow-Water Equation with Initial-Boundary Value and Their Numerical Experiment[J]. Applied Mathematics and Mechanics, 1989, 10(3): 259-269.

浅水方程初边值问题几种新的差分格式及其数值试验

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.
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    [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.
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出版历程
  • 收稿日期:  1986-11-08
  • 刊出日期:  1989-03-15

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