The Shallow Water Wave Equations: Formulation, Analysis and Application

摘要: I. Introduction.- Areas of Application for the Shallow Water Equations.- Finite Element Methods Solution Analyzing Spatial Oscillations in Numerical Schemes.- Stability II. Equation Formulation.- Primitive Form.- Wave Generalized Linearized Form Continuity and Momentum III. Fourier Analysis Methods.- Analysis: An Accuracy Measure.- Amplitude Propagation Factors Arising from Second Degree Polynomials.- IV. Stability.- General Concepts.- Routh-Hurwitz Lienard-Chipart.- Orlando.- Factorization Higher Polynomials into Lower Determination a Product V. Explicit Using Various Discretizations.- Equal Node Spacing Constant Bathymetry One Dimension.- to Unequal Spacing.- Applications with Even Variable Bathymetry.- Rectangular Grid.- VI. Implicit Reducing Number Time Dependent Terms Matrix Equation.- Treatment Coriolis Term an Repeated Back Substitutions Replacing Decompositions.- The VII. Oscillations.- N-Dimensional Uniform Nonuniform Grid Multi-Information Nodes.- Leapfrog Scheme Formulation on Linear Elements.- Quadratic Use Dispersion Evaluating 2?x Test: Assessing Ability Suppress Node-to-Node VIII. Temporal Artifacts.- A Different Three Level Approximation Two IX. Applications.- Quarter Circle Harbor.- Southern Part North Sea - I.- II.- X. Conclusions.- A. Equivalent Formulations Conditions Which Guarantee Roots Magnitude Less than Unity.