Numerical Methods For Shallow Water Flow

Author : C.B. Vreugdenhil
Publisher : Springer Science & Business Media
Page : 273 pages
File Size : 49,9 Mb
Release : 2013-03-09
Category : Science
ISBN : 9789401583541

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Numerical Methods for Shallow-Water Flow by C.B. Vreugdenhil Pdf

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.

Author : W.Y. Tan
Publisher : Elsevier
Page : 433 pages
File Size : 42,7 Mb
Release : 1992-08-17
Category : Science
ISBN : 0080870937

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Shallow Water Hydrodynamics by W.Y. Tan Pdf

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.

Author : Jian Guo Zhou
Publisher : Springer Science & Business Media
Page : 118 pages
File Size : 53,5 Mb
Release : 2013-03-14
Category : Science
ISBN : 9783662082768

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Lattice Boltzmann Methods for Shallow Water Flows by Jian Guo Zhou Pdf

The lattice Boltzmann method (LBM) is a modern numerical technique, very efficient, flexible to simulate different flows within complex/varying geome tries. It is evolved from the lattice gas automata (LGA) in order to overcome the difficulties with the LGA. The core equation in the LBM turns out to be a special discrete form of the continuum Boltzmann equation, leading it to be self-explanatory in statistical physics. The method describes the micro scopic picture of particles movement in an extremely simplified way, and on the macroscopic level it gives a correct average description of a fluid. The av eraged particle velocities behave in time and space just as the flow velocities in a physical fluid, showing a direct link between discrete microscopic and continuum macroscopic phenomena. In contrast to the traditional computational fluid dynamics (CFD) based on a direct solution of flow equations, the lattice Boltzmann method provides an indirect way for solution of the flow equations. The method is characterized by simple calculation, parallel process and easy implementation of boundary conditions. It is these features that make the lattice Boltzmann method a very promising computational method in different areas. In recent years, it receives extensive attentions and becomes a very potential research area in computational fluid dynamics. However, most published books are limited to the lattice Boltzmann methods for the Navier-Stokes equations. On the other hand, shallow water flows exist in many practical situations such as tidal flows, waves, open channel flows and dam-break flows.

Author : F. W. Wubs
Publisher : Unknown
Page : 130 pages
File Size : 48,6 Mb
Release : 1988
Category : CYBER 205 (Computer).
ISBN : UOM:39015013835502

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Numerical Solution of the Shallow-water Equations by F. W. Wubs Pdf

Author : Gayaz Khakimzyanov,Denys Dutykh,Zinaida Fedotova,Oleg Gusev
Publisher : Springer Nature
Page : 296 pages
File Size : 51,9 Mb
Release : 2020-09-15
Category : Mathematics
ISBN : 9783030462673

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Dispersive Shallow Water Waves by Gayaz Khakimzyanov,Denys Dutykh,Zinaida Fedotova,Oleg Gusev Pdf

This monograph presents cutting-edge research on dispersive wave modelling, and the numerical methods used to simulate the propagation and generation of long surface water waves. Including both an overview of existing dispersive models, as well as recent breakthroughs, the authors maintain an ideal balance between theory and applications. From modelling tsunami waves to smaller scale coastal processes, this book will be an indispensable resource for those looking to be brought up-to-date in this active area of scientific research. Beginning with an introduction to various dispersive long wave models on the flat space, the authors establish a foundation on which readers can confidently approach more advanced mathematical models and numerical techniques. The first two chapters of the book cover modelling and numerical simulation over globally flat spaces, including adaptive moving grid methods along with the operator splitting approach, which was historically proposed at the Institute of Computational Technologies at Novosibirsk. Later chapters build on this to explore high-end mathematical modelling of the fluid flow over deformed and rotating spheres using the operator splitting approach. The appendices that follow further elaborate by providing valuable insight into long wave models based on the potential flow assumption, and modified intermediate weakly nonlinear weakly dispersive equations. Dispersive Shallow Water Waves will be a valuable resource for researchers studying theoretical or applied oceanography, nonlinear waves as well as those more broadly interested in free surface flow dynamics.

Author : Abdul A. Khan,Wencong Lai
Publisher : CRC Press
Page : 208 pages
File Size : 48,7 Mb
Release : 2014-03-03
Category : Science
ISBN : 9781482226027

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Modeling Shallow Water Flows Using the Discontinuous Galerkin Method by Abdul A. Khan,Wencong Lai Pdf

Replacing the Traditional Physical Model ApproachComputational models offer promise in improving the modeling of shallow water flows. As new techniques are considered, the process continues to change and evolve. Modeling Shallow Water Flows Using the Discontinuous Galerkin Method examines a technique that focuses on hyperbolic conservation l

Author : W. L. Wood
Publisher : Oxford University Press
Page : 290 pages
File Size : 44,6 Mb
Release : 1993
Category : Mathematics
ISBN : 0198596901

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Introduction to Numerical Methods for Water Resources by W. L. Wood Pdf

Numerical methods provide a powerful and essential tool for the solution of problems of water resources. This book gives an elementary introduction to the various methods in current use and demonstrates that different methods work well in different situations and some problems requirecombinations of methods. It is essential to know something of all of them in order to make a reasoned judgement of current practice. Their applications are discussed and more specialised versions are outlined along with many references making this an invaluable, comprehensive coverage of thefield.

Author : Gerhard H. Jirka,Wim S.J. Uijttewaal
Publisher : CRC Press
Page : 692 pages
File Size : 43,6 Mb
Release : 2004-09-15
Category : Science
ISBN : 0203027329

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Shallow Flows by Gerhard H. Jirka,Wim S.J. Uijttewaal Pdf

This text presents the key findings of the International Symposium held in Delft in 2003, which explored the process of shallow flows. Shallow flows are found in lowland rivers, lakes, estuaries, bays, coastal areas and in density-stratified atmospheres, and may be observed in puddles, as in oceans. They impact on the life and work of a w

Author : Abdul A. Khan,Wencong Lai
Publisher : CRC Press
Page : 218 pages
File Size : 43,9 Mb
Release : 2014-03-03
Category : Science
ISBN : 9781482226010

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Modeling Shallow Water Flows Using the Discontinuous Galerkin Method by Abdul A. Khan,Wencong Lai Pdf

Replacing the Traditional Physical Model Approach Computational models offer promise in improving the modeling of shallow water flows. As new techniques are considered, the process continues to change and evolve. Modeling Shallow Water Flows Using the Discontinuous Galerkin Method examines a technique that focuses on hyperbolic conservation laws and includes one-dimensional and two-dimensional shallow water flows and pollutant transports. Combines the Advantages of Finite Volume and Finite Element Methods This book explores the discontinuous Galerkin (DG) method, also known as the discontinuous finite element method, in depth. It introduces the DG method and its application to shallow water flows, as well as background information for implementing and applying this method for natural rivers. It considers dam-break problems, shock wave problems, and flows in different regimes (subcritical, supercritical, and transcritical). Readily Adaptable to the Real World While the DG method has been widely used in the fields of science and engineering, its use for hydraulics has so far been limited to simple cases. The book compares numerical results with laboratory experiments and field data, and includes a set of tests that can be used for a wide range of applications. Provides step-by-step implementation details Presents the different forms in which the shallow water flow equations can be written Places emphasis on the details and modifications required to apply the scheme to real-world flow problems This text enables readers to readily understand and develop an efficient computer simulation model that can be used to model flow, contaminant transport, and other aspects in rivers and coastal environments. It is an ideal resource for practicing environmental engineers and researchers in the area of computational hydraulics and fluid dynamics, and graduate students in computational hydraulics.

Author : G. S. Stelling
Publisher : Unknown
Page : 226 pages
File Size : 47,5 Mb
Release : 1984
Category : Difference equations
ISBN : 9012043662

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On the Construction of Computational Methods for Shallow Water Flow Problems by G. S. Stelling Pdf

Author : Harald van Brummelen,Alessandro Corsini,Simona Perotto,Gianluigi Rozza
Publisher : Springer Nature
Page : 358 pages
File Size : 40,8 Mb
Release : 2020-02-22
Category : Mathematics
ISBN : 9783030307059

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Numerical Methods for Flows by Harald van Brummelen,Alessandro Corsini,Simona Perotto,Gianluigi Rozza Pdf

This book includes selected contributions on applied mathematics, numerical analysis, numerical simulation and scientific computing related to fluid mechanics problems, presented at the FEF-“Finite Element for Flows” conference, held in Rome in spring 2017. Written by leading international experts and covering state-of-the-art topics in numerical simulation for flows, it provides fascinating insights into and perspectives on current and future methodological and numerical developments in computational science. As such, the book is a valuable resource for researchers, as well as Masters and Ph.D students.

Author : Oscar Castro-Orgaz,Willi H. Hager
Publisher : Springer Nature
Page : 563 pages
File Size : 49,8 Mb
Release : 2019-11-08
Category : Mathematics
ISBN : 9783030130732

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Shallow Water Hydraulics by Oscar Castro-Orgaz,Willi H. Hager Pdf

This book presents the theory and computation of open channel flows, using detailed analytical, numerical and experimental results. The fundamental equations of open channel flows are derived by means of a rigorous vertical integration of the RANS equations for turbulent flow. In turn, the hydrostatic pressure hypothesis, which forms the core of many shallow water hydraulic models, is scrutinized by analyzing its underlying assumptions. The book’s main focus is on one-dimensional models, including detailed treatments of unsteady and steady flows. The use of modern shock capturing finite difference and finite volume methods is described in detail, and the quality of solutions is carefully assessed on the basis of analytical and experimental results. The book’s unique features include: • Rigorous derivation of the hydrostatic-based shallow water hydraulic models • Detailed treatment of steady open channel flows, including the computation of transcritical flow profiles • General analysis of gate maneuvers as the solution of a Riemann problem • Presents modern shock capturing finite volume methods for the computation of unsteady free surface flows • Introduces readers to movable bed and sediment transport in shallow water models • Includes numerical solutions of shallow water hydraulic models for non-hydrostatic steady and unsteady free surface flows This book is suitable for both undergraduate and graduate level students, given that the theory and numerical methods are progressively introduced starting with the basics. As supporting material, a collection of source codes written in Visual Basic and inserted as macros in Microsoft Excel® is available. The theory is implemented step-by-step in the codes, and the resulting programs are used throughout the book to produce the respective solutions.

Author : A.G. Kulikovskii,N.V. Pogorelov,A. Yu. Semenov
Publisher : CRC Press
Page : 564 pages
File Size : 40,6 Mb
Release : 2000-12-21
Category : Mathematics
ISBN : 0849306086

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Mathematical Aspects of Numerical Solution of Hyperbolic Systems by A.G. Kulikovskii,N.V. Pogorelov,A. Yu. Semenov Pdf

This important new book sets forth a comprehensive description of various mathematical aspects of problems originating in numerical solution of hyperbolic systems of partial differential equations. The authors present the material in the context of the important mechanical applications of such systems, including the Euler equations of gas dynamics, magnetohydrodynamics (MHD), shallow water, and solid dynamics equations. This treatment provides-for the first time in book form-a collection of recipes for applying higher-order non-oscillatory shock-capturing schemes to MHD modelling of physical phenomena. The authors also address a number of original "nonclassical" problems, such as shock wave propagation in rods and composite materials, ionization fronts in plasma, and electromagnetic shock waves in magnets. They show that if a small-scale, higher-order mathematical model results in oscillations of the discontinuity structure, the variety of admissible discontinuities can exhibit disperse behavior, including some with additional boundary conditions that do not follow from the hyperbolic conservation laws. Nonclassical problems are accompanied by a multiple nonuniqueness of solutions. The authors formulate several selection rules, which in some cases easily allow a correct, physically realizable choice. This work systematizes methods for overcoming the difficulties inherent in the solution of hyperbolic systems. Its unique focus on applications, both traditional and new, makes Mathematical Aspects of Numerical Solution of Hyperbolic Systems particularly valuable not only to those interested the development of numerical methods, but to physicists and engineers who strive to solve increasingly complicated nonlinear equations.

Author : Wei-Yan Tan
Publisher : Unknown
Page : 434 pages
File Size : 47,5 Mb
Release : 1992
Category : Fluid dynamics
ISBN : 0444416234

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Shallow Water Hydrodynamics by Wei-Yan Tan Pdf

Author : Elena Vázquez-Cendón,Arturo Hidalgo,Pilar Garcia Navarro,Luis Cea
Publisher : CRC Press
Page : 434 pages
File Size : 44,8 Mb
Release : 2012-11-05
Category : Mathematics
ISBN : 9780203562338

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Numerical Methods for Hyperbolic Equations by Elena Vázquez-Cendón,Arturo Hidalgo,Pilar Garcia Navarro,Luis Cea Pdf

Numerical Methods for Hyperbolic Equations is a collection of 49 articles presented at the International Conference on Numerical Methods for Hyperbolic Equations: Theory and Applications (Santiago de Compostela, Spain, 4-8 July 2011). The conference was organized to honour Professor Eleuterio Toro in the month of his 65th birthday. The topics cover