Download or read book Waiting time solutions of the shallow water equations written by R E. Grundy and published by . This book was released on 1993 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Shallow Water Wave Equations Formulation Analysis and Application written by Ingemar Kinnmark and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Shallow Water Hydrodynamics written by W.Y. Tan and published by Elsevier. This book was released on 1992-08-17 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: Within this monograph a comprehensive and systematic knowledge on shallow-water hydrodynamics is presented. A two-dimensional system of shallow-water equations is analyzed, including the mathematical and mechanical backgrounds, the properties of the system and its solution. Also featured is a new mathematical simulation of shallow-water flows by compressible plane flows of a special virtual perfect gas, as well as practical algorithms such as FDM, FEM, and FVM. Some of these algorithms have been utilized in solving the system, while others have been utilized in various applied fields. An emphasis has been placed on several classes of high-performance difference schemes and boundary procedures which have found wide uses recently for solving the Euler equations of gas dynamics in aeronautical and aerospatial engineering. This book is constructed so that it may serve as a handbook for practicians. It will be of interest to scientists, designers, teachers, postgraduates and professionals in hydraulic, marine, and environmental engineering; especially those involved in the mathematical modelling of shallow-water bodies.
Download or read book Lie Group Analysis of Solutions of Shallow Water Equations written by Melanie Sanders and published by . This book was released on 2011 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Similarity Solutions of the Shallow Water Equations written by P. Glaister and published by . This book was released on 1991 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Solution of the Shallow water Equations written by F. W. Wubs and published by . This book was released on 1988 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Towards Efficient Techniques for Solutions of the Shallow Water Equations written by Owen Thomas DeGennaro-Ransom and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Research was conducted in order to develop more efficient solution techniques for the Shallow Water Equations (SWE) for naturally occurring free-surface flows in natural and engineered channels. Methods relating to numerical solution of the two-dimensional equations utilizing graphical processing units (GPU) as the main computational device and combined one-and two-dimensional schemes are presented and tested. Different numerical methods were investigated for inclusion to the model. General requirements for the proposed schemes included the ability to be solved using a finite-difference conservative solution algorithm on a fixed rectangular grid and the ability to both withstand and provide reasonable approximation of shocks and bores within the solution domain. Two such schemes were investigated that met initial criteria: A graphical processing unit (GPU) implementation of the well established MacCormack method, and a selectively under-relaxed implicit method. Both methods included the addition of a TVD (total variation diminishing) term to help maintain stability around high gradient flow areas.The implicit method incorporates an algorithm for selectively under-relaxing the iterative process to maintain stability in the presence of shock interfaces. The value of the Courant number and the frequency at which the TVD term was incorporated were constantly updated during the computation to achieve optimal speed of execution while maintaining stability. The method was tested against published results from experiments and from computations employing alternative algorithms and the results obtained demonstrate both the economy and accuracy of the proposed algorithm. The MacCormack-based scheme was chosen for both optimizing procedure attempts. Methodology was tested that allowed for one and two-dimensional TVD-MacCormack equation coupling, reducing grid-size dependency for the solution domain, while permitting simultaneous calculation of both one and two dimensional domains, and the explicit, finite-difference formulation of the solution methodology was well suited for inclusion into simultaneous GPU calculation. Cell alignment and cell-neighbor management is shifted from matrix to array form, which allows for a new framework, optimally constructed for inclusion of the dimensionally coupled solution scheme. The code contains adaptive time-stepping, based on maximum local Courant number, and special wetting/drying schemes to maximize stability while maintaining accuracy. The method was tested against published results, showing it's effectiveness in minimizing computational resources while comparing well with experimentally derived results. The coupled code is tempered for insertion into a parallel computing array. Ultimately, while dimensional coupling provided a slight optimization in terms of computational efficiency, the dimensional interface methodology and limited domain types the solution technique was constructed for restrict it to a specific-use tool. The extension of the MacCormack method to GPU processing ultimately proved more useful, showing speed increases of 4-40 times depending on the domains geomorphological characteristics.
Download or read book A Solution of the Axisymmetric Shallow Water Equations written by Edward Francis Staab and published by . This book was released on 1979 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Difference Solutions of the Shallow water Equation written by James A. Liggett and published by . This book was released on 1967 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Difference Solutions of the Shallow water Equation written by James A. Liggett and published by . This book was released on 1967 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Computational Algorithms for Shallow Water Equations written by Eleuterio F. Toro and published by Springer Nature. This book was released on with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Methods for Shallow Water Flow written by C.B. Vreugdenhil and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book On the Stability of Spreading Pool Solutions of the Shallow Water Equations written by D. M. Webber and published by . This book was released on 1992 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Solution of the Shallow Water Equations written by David L. Whitfield and published by . This book was released on 1996 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Finite Element Solution of the Shallow Water Equations written by Daniel Roger Lynch and published by . This book was released on 1978 with total page 698 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Global Existence of Solutions for the Viscous Shallow Water Equations written by Linda Ethel Sundbye and published by . This book was released on 1994 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Solution of the Shallow water Equations written by Friederik Wilhelm Wubs and published by . This book was released on 1987 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt:
