The Shallow Water Wave Equations: Formulation, Analysis and Application
The Shallow Water Wave Equations: Formulation, Analysis and Application
复制标题
DOI：
10.2307/2008784
复制
发表时间：
1985-12
期刊：
影响因子：
--
通讯作者：
Ingemar Kinnmark
中科院分区：
文献类型：
--
作者：
Ingemar Kinnmark
I.介绍。浅水方程的应用领域。浅水方程的有限元素法数值格式中空间振荡的分析方法数值格式的稳定性分析方法二.公式化。原始方程形式。波动方程形式广义波动方程形式连续性方程和动量方程的线性化形式。三.傅立叶分析方法傅立叶分析：一种精确的测量方法。由二次多项式引起的传播因子的幅度。四.稳定。-一般概念。Routh-Hurwitz和Lienard-Chipart。劳斯-赫维茨和奥兰多高次多项式分解为低次多项式多项式乘积的稳定性判定V.使用各种空间离散化的显式方法。等节点间距和一维恒定水深。应用于不相等的节点间距。均匀节点间距和可变水深测量的应用。应用于矩形网格。六.隐式方法。减少波动方程矩阵中与时间相关的项的数量。隐式波连续性方程中科里奥利项的显式处理重复的回代替换分解。广义波动连续性方程七.空间震荡。N维均匀矩形网格多信息结点的N维非均匀矩形网格线性单元上的蛙跳格式和波动方程蛙跳格式和二次元素上的波动方程频散分析在评价数值格式中的应用2号？x测试：评估抑制节点到节点振荡的能力。八.时间振荡。数字文物。-动量方程的一种不同的三时间水平近似。动量方程的两个时间级近似九.应用程序。关于Quarter Circle Harbor适用于北海南部- I.-适用于北海南部- II。X.结论。A.保证大小根小于单位的条件的等价公式。
I. Introduction.- Areas of Application for the Shallow Water Equations.- Finite Element Methods for Solution of the Shallow Water Equations.- Methods for Analyzing Spatial Oscillations in Numerical Schemes.- Methods for Analyzing Stability of Numerical Schemes.- II. Equation Formulation.- Primitive Equation Form.- Wave Equation Form.- Generalized Wave Equation Form.- Linearized Form of the Continuity and Momentum Equations.- III. Fourier Analysis Methods.- Fourier Analysis: An Accuracy Measure.- Amplitude of Propagation Factors Arising from Second Degree Polynomials.- IV. Stability.- General Concepts.- Routh-Hurwitz and Lienard-Chipart.- Routh-Hurwitz and Orlando.- Factorization of Higher Degree Polynomials into Lower Degree Polynomials.- Determination of Stability for a Product of Polynomials.- V. Explicit Methods Using Various Spatial Discretizations.- Equal Node Spacing and Constant Bathymetry in One Dimension.- Application to Unequal Node Spacing.- Applications with Even Node Spacing and Variable Bathymetry.- Application to a Rectangular Grid.- VI. Implicit Methods.- Reducing the Number of Time Dependent Terms in the Matrix for the Wave Equation.- Explicit Treatment of the Coriolis Term in an Implicit Wave Continuity Equation.- Repeated Back Substitutions Replacing Decompositions.- The Generalized Wave Continuity Equation.- VII. Spatial Oscillations.- N-Dimensional Uniform Rectangular Grid.- N-Dimensional Nonuniform Rectangular Grid with Multi-Information Nodes.- Leapfrog Scheme and Wave Equation Formulation on Linear Elements.- Leapfrog Scheme and Wave Equation Formulation on Quadratic Elements.- The Use of Dispersion Analysis in Evaluating Numerical Schemes.- The 2?x Test: Assessing the Ability to Suppress Node-to-Node Oscillations.- VIII. Temporal Oscillations.- Numerical Artifacts.- A Different Three Time Level Approximation of the Momentum Equations.- A Two Time Level Approximation of the Momentum Equations.- IX. Applications.- Application to Quarter Circle Harbor.- Application to the Southern Part of the North Sea - I.- Application to the Southern Part of the North Sea - II.- X. Conclusions.- A. Equivalent Formulations of Conditions Which Guarantee Roots of Magnitude Less than Unity.