Shock-Capturing Methods for Free-Surface Shallow Flows PDF Download
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Author: E. F. Toro
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 336
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Book Description
The first of its kind in the field, this title examines the use of modern, shock-capturing finite volume numerical methods, in the solution of partial differential equations associated with free-surface flows, which satisfy the shallow-water type assumption (including shallow water flows, dense gases and mixtures of materials as special samples). Starting with a general presentation of the governing equations for free-surface shallow flows and a discussion of their physical applicability, the book goes on to analyse the mathematical properties of the equations, in preparation for the presentation of the exact solution of the Riemann problem for wet and dry beds. After a general introduction to the finite volume approach, several chapters are then devoted to describing a variety of modern shock-capturing finite volume numerical methods, including Godunov methods of the upwind and centred type. Approximate Riemann solvers following various approaches are studied in detail as is their use in the Godunov approach for constructing low and high-order upwind TVD methods. Centred TVD schemes are also presented. Two chapters are then devoted to practical applications. The book finishes with an overview of potential practical applications of the methods studied, along with appropriate reference to sources of further information. Features include: * Algorithmic and practical presentation of the methods * Practical applications such as dam-break modelling and the study of bore reflection patterns in two space dimensions * Sample computer programs and accompanying numerical software (details available at www.numeritek.com) The book is suitable for teaching postgraduate students of civil, mechanical, hydraulic and environmental engineering, meteorology, oceanography, fluid mechanics and applied mathematics. Selected portions of the material may also be useful in teaching final year undergraduate students in the above disciplines. The contents will also be of interest to research scientists and engineers in academia and research and consultancy laboratories.
Author: E. F. Toro
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 336
Get Book Here
Book Description
The first of its kind in the field, this title examines the use of modern, shock-capturing finite volume numerical methods, in the solution of partial differential equations associated with free-surface flows, which satisfy the shallow-water type assumption (including shallow water flows, dense gases and mixtures of materials as special samples). Starting with a general presentation of the governing equations for free-surface shallow flows and a discussion of their physical applicability, the book goes on to analyse the mathematical properties of the equations, in preparation for the presentation of the exact solution of the Riemann problem for wet and dry beds. After a general introduction to the finite volume approach, several chapters are then devoted to describing a variety of modern shock-capturing finite volume numerical methods, including Godunov methods of the upwind and centred type. Approximate Riemann solvers following various approaches are studied in detail as is their use in the Godunov approach for constructing low and high-order upwind TVD methods. Centred TVD schemes are also presented. Two chapters are then devoted to practical applications. The book finishes with an overview of potential practical applications of the methods studied, along with appropriate reference to sources of further information. Features include: * Algorithmic and practical presentation of the methods * Practical applications such as dam-break modelling and the study of bore reflection patterns in two space dimensions * Sample computer programs and accompanying numerical software (details available at www.numeritek.com) The book is suitable for teaching postgraduate students of civil, mechanical, hydraulic and environmental engineering, meteorology, oceanography, fluid mechanics and applied mathematics. Selected portions of the material may also be useful in teaching final year undergraduate students in the above disciplines. The contents will also be of interest to research scientists and engineers in academia and research and consultancy laboratories.
Author: Gerhard H. Jirka
Publisher: CRC Press
ISBN: 9780203027325
Category : Science
Languages : en
Pages : 692
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Book Description
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: Oscar Castro-Orgaz
Publisher: Springer
ISBN: 3319479717
Category : Science
Languages : en
Pages : 699
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Book Description
This book provides essential information on the higher mathematical level of approximation over the gradually varied flow theory, also referred to as the Boussinesq-type theory. In this context, it presents higher order flow equations, together with their applications in a broad range of pertinent engineering and environmental problems, including open channel, groundwater, and granular material flows.
Author: Barry Koren
Publisher: Springer Science & Business Media
ISBN: 3642033873
Category : Mathematics
Languages : en
Pages : 501
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Book Description
The aim of the present book is to show, in a broad and yet deep way, the state of the art in computational science and engineering. Examples of topics addressed are: fast and accurate numerical algorithms, model-order reduction, grid computing, immersed-boundary methods, and specific computational methods for simulating a wide variety of challenging problems, problems such as: fluid-structure interaction, turbulent flames, bone-fracture healing, micro-electro-mechanical systems, failure of composite materials, storm surges, particulate flows, and so on. The main benefit offered to readers of the book is a well-balanced, up-to-date overview over the field of computational science and engineering, through in-depth articles by specialists from the separate disciplines.
Author: Oscar Castro-Orgaz
Publisher: Springer Nature
ISBN: 3030130738
Category : Mathematics
Languages : en
Pages : 572
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Book Description
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: Mohamed Atef Helal
Publisher: Springer Nature
ISBN: 1071624571
Category : Science
Languages : en
Pages : 483
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Book Description
This newly updated volume of the Encyclopedia of Complexity and Systems Science (ECSS) presents several mathematical models that describe this physical phenomenon, including the famous non-linear equation Korteweg-de-Vries (KdV) that represents the canonical form of solitons. Also, there exists a class of nonlinear partial differential equations that led to solitons, e.g., Kadomtsev-Petviashvili (KP), Klein-Gordon (KG), Sine-Gordon (SG), Non-Linear Schrödinger (NLS), Korteweg-de-Vries Burger’s (KdVB), etc. Different linear mathematical methods can be used to solve these models analytically, such as the Inverse Scattering Transformation (IST), Adomian Decomposition Method, Variational Iteration Method (VIM), Homotopy Analysis Method (HAM) and Homotopy Perturbation Method (HPM). Other non-analytic methods use the computational techniques available in such popular mathematical packages as Mathematica, Maple, and MATLAB. The main purpose of this volume is to provide physicists, engineers, and their students with the proper methods and tools to solve the soliton equations, and to discover the new possibilities of using solitons in multi-disciplinary areas ranging from telecommunications to biology, cosmology, and oceanographic studies.
Author: Massimo Greco
Publisher: CRC Press
ISBN: 1482298341
Category : Science
Languages : en
Pages : 1469
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Book Description
RiverFlow 2004 is the Second International Conference on Fluvial Hydraulics, organized as speciality conferences under the auspices of the International Association of Hydraulic Engineering and Research (IAHR) within its Fluvial Hydraulics and Eco Hydraulics Sections. RiverFlow conferences are a significant forum of discussion for many researchers
Author: Xinming Tang
Publisher: CRC Press
ISBN: 0415408156
Category : Science
Languages : en
Pages : 2385
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Book Description
Developments in Geographic Information Technology have raised the expectations of users. A static map is no longer enough; there is now demand for a dynamic representation. Time is of great importance when operating on real world geographical phenomena, especially when these are dynamic. Researchers in the field of Temporal Geographical Information Systems (TGIS) have been developing methods of incorporating time into geographical information systems. Spatio-temporal analysis embodies spatial modelling, spatio-temporal modelling and spatial reasoning and data mining. Advances in Spatio-Temporal Analysis contributes to the field of spatio-temporal analysis, presenting innovative ideas and examples that reflect current progress and achievements.
Author: Jurjen A. Battjes
Publisher: Cambridge University Press
ISBN: 1316982734
Category : Science
Languages : en
Pages : 309
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Book Description
Practitioners in water engineering rely on a thorough understanding of shallow water flows in order to safeguard our habitat, while at the same time sustaining the water environment. This book proposes a unified theoretical framework for the different types of shallow flow, providing a coherent approach to interpret the behaviour of such flows, and highlighting the similarities and differences. Every major topic in the book is accompanied by worked examples illustrating the theoretical concepts. Practical examples, showcasing inspiring research and engineering applications from the past and present, provide insight into how the theory developed. The book is also supplemented by a range of online resources, available at www.cambridge.org/battjes, including problem sets and computer codes. A solutions manual is available for instructors. This book is intended for students and professionals working in environmental water systems, in areas such as coasts, rivers, harbours, drainage, and irrigation canals.
Author: Mingfu Guan
Publisher: Frontiers Media SA
ISBN: 2889668428
Category : Science
Languages : en
Pages : 148
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Book Description
