The Shallow Water Wave Equations Formulation Analysis And Application
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The Shallow Water Wave Equations Formulation Analysis and Application
Author | : Ingemar Kinnmark |
Publsiher | : Springer Science & Business Media |
Total Pages | : 212 |
Release | : 2012-12-06 |
Genre | : Science |
ISBN | : 9783642826467 |
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1. 1 AREAS OF APPLICATION FOR THE SHALLOW WATER EQUATIONS The shallow water equations describe conservation of mass and mo mentum in a fluid. They may be expressed in the primitive equation form Continuity Equation _ a, + V. (Hv) = 0 L(l;,v;h) at (1. 1) Non-Conservative Momentum Equations a M("vjt,f,g,h,A) = at(v) + (v. V)v + tv - fkxv + gV, - AIH = 0 (1. 2) 2 where is elevation above a datum (L) ~ h is bathymetry (L) H = h + C is total fluid depth (L) v is vertically averaged fluid velocity in eastward direction (x) and northward direction (y) (LIT) t is the non-linear friction coefficient (liT) f is the Coriolis parameter (liT) is acceleration due to gravity (L/T2) g A is atmospheric (wind) forcing in eastward direction (x) and northward direction (y) (L2/T2) v is the gradient operator (IlL) k is a unit vector in the vertical direction (1) x is positive eastward (L) is positive northward (L) Y t is time (T) These Non-Conservative Momentum Equations may be compared to the Conservative Momentum Equations (2. 4). The latter originate directly from a vertical integration of a momentum balance over a fluid ele ment. The former are obtained indirectly, through subtraction of the continuity equation from the latter. Equations (1. 1) and (1. 2) are valid under the following assumptions: 1. The fluid is well-mixed vertically with a hydrostatic pressure gradient. 2. The density of the fluid is constant.
Numerical Methods for Shallow Water Flow
Author | : C.B. Vreugdenhil |
Publsiher | : Springer Science & Business Media |
Total Pages | : 273 |
Release | : 2013-03-09 |
Genre | : Science |
ISBN | : 9789401583541 |
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A wide variety of problems are associated with the flow of shallow water, such as atmospheric flows, tides, storm surges, river and coastal flows, lake flows, tsunamis. Numerical simulation is an effective tool in solving them and a great variety of numerical methods are available. The first part of the book summarizes the basic physics of shallow-water flow needed to use numerical methods under various conditions. The second part gives an overview of possible numerical methods, together with their stability and accuracy properties as well as with an assessment of their performance under various conditions. This enables the reader to select a method for particular applications. Correct treatment of boundary conditions (often neglected) is emphasized. The major part of the book is about two-dimensional shallow-water equations but a discussion of the 3-D form is included. The book is intended for researchers and users of shallow-water models in oceanographic and meteorological institutes, hydraulic engineering and consulting. It also provides a major source of information for applied and numerical mathematicians.
Analysis of the Numerical Solution of the Shallow Water Equations
![Analysis of the Numerical Solution of the Shallow Water Equations](https://youbookinc.com/wp-content/uploads/2024/06/cover.jpg)
Author | : Thomas A. Hamrick,Naval Postgraduate School (U.S.) |
Publsiher | : Unknown |
Total Pages | : 86 |
Release | : 1997-09-01 |
Genre | : Electronic Book |
ISBN | : 1423565703 |
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This thesis is concerned with the analysis of various methods for the numerical solution of the shallow water equations along with the stability of these methods. Most of the thesis is concerned with the background and formaulation of the shallow water equations. The derivation of the basic equations will be given, in the primative variable and vorticity divergence formulation. Also the shallow water equations will be written in spherical coordinates. Two main types of methods used in approximating differential equations of this nature will be discussed. The two schemes are finite difference method (FDM) and the finite element method (FEM). After presenting the shallow water equations in several formulations, some examples will be presented. The use of the Fourier transform to find the solution of a semidiscrete analog of the shallow water equations is also demonstrated.
Water Waves
Author | : J. J. Stoker |
Publsiher | : John Wiley & Sons |
Total Pages | : 598 |
Release | : 2011-08-15 |
Genre | : Mathematics |
ISBN | : 9781118031353 |
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Offers an integrated account of the mathematical hypothesis of wave motion in liquids with a free surface, subjected to gravitational and other forces. Uses both potential and linear wave equation theories, together with applications such as the Laplace and Fourier transform methods, conformal mapping and complex variable techniques in general or integral equations, methods employing a Green's function. Coverage includes fundamental hydrodynamics, waves on sloping beaches, problems involving waves in shallow water, the motion of ships and much more.
Selected Papers from the 14th Estuarine and Coastal Modeling Conference
Author | : Richard P. Signell |
Publsiher | : MDPI |
Total Pages | : 421 |
Release | : 2018-06-27 |
Genre | : Electronic book |
ISBN | : 9783038423621 |
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This book is a printed edition of the Special Issue "Selected Papers from the 14th Estuarine and Coastal Modeling Conference" that was published in JMSE
Applied mechanics reviews
Author | : Anonim |
Publsiher | : Unknown |
Total Pages | : 400 |
Release | : 1948 |
Genre | : Mechanics, Applied |
ISBN | : OSU:32435026160655 |
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The Water Waves Problem
Author | : David Lannes |
Publsiher | : American Mathematical Soc. |
Total Pages | : 347 |
Release | : 2013-05-08 |
Genre | : Mathematics |
ISBN | : 9780821894705 |
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This monograph provides a comprehensive and self-contained study on the theory of water waves equations, a research area that has been very active in recent years. The vast literature devoted to the study of water waves offers numerous asymptotic models.
Energy Science and Applied Technology ESAT 2016
Author | : Zhigang Fang |
Publsiher | : CRC Press |
Total Pages | : 794 |
Release | : 2016-10-14 |
Genre | : Science |
ISBN | : 9781498779227 |
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The 2016 International Conference on Energy Science and Applied Technology (ESAT 2016) held on June 25-26 in Wuhan, China aimed to provide a platform for researchers, engineers, and academicians, as well as industrial professionals, to present their research results and development activities in energy science and engineering and its applied technology. The themes presented in Energy Science and Applied Technology ESAT 2016 are: Technologies in Geology, Mining, Oil and Gas; Renewable Energy, Bio-Energy and Cell Technologies; Energy Transfer and Conversion, Materials and Chemical Technologies; Environmental Engineering and Sustainable Development; Electrical and Electronic Technology, Power System Engineering; Mechanical, Manufacturing, Process Engineering; Control and Automation; Communications and Applied Information Technologies; Applied and Computational Mathematics; Methods and Algorithms Optimization; Network Technology and Application; System Test, Diagnosis, Detection and Monitoring; Recognition, Video and Image Processing.