The shallow water wave equations : formulation, analysis, and application  U.S. ~ Berlin

I. Kinnmark

[目次]

  • 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.

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この本の情報

書名 The shallow water wave equations : formulation, analysis, and application
著作者等 Kinnmark, I.
Kinnmark Ingemar
Kinnmark I
シリーズ名 Lecture notes in engineering
巻冊次 U.S.
Berlin
出版元 Springer-Verlag
刊行年月 c1986
版表示 Softcover reprint of the original 1st ed. 1986
ページ数 xxv, 187 p.
大きさ 25 cm
ISBN 3540160310
0387160310
NCID BA01066187
※クリックでCiNii Booksを表示
言語 英語
出版国 ドイツ
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