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Author: C.B. Vreugdenhil Publisher: Springer Science & Business Media ISBN: 9401583544 Category : Science Languages : en Pages : 273
Book Description
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: C.B. Vreugdenhil Publisher: Springer Science & Business Media ISBN: 9401583544 Category : Science Languages : en Pages : 273
Book Description
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 ISBN: 9780080870939 Category : Science Languages : en Pages : 433
Book Description
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 ISBN: 3662082764 Category : Science Languages : en Pages : 118
Book Description
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: Gerhard H. Jirka Publisher: CRC Press ISBN: 9780203027325 Category : Science Languages : en Pages : 692
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: Gayaz Khakimzyanov Publisher: Springer Nature ISBN: 3030462676 Category : Mathematics Languages : en Pages : 296
Book Description
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 Publisher: CRC Press ISBN: 1482226022 Category : Science Languages : en Pages : 208
Book Description
This book introduces the discontinuous Galerkin (DG) method and its application to shallow water flows. The emphasis is to show details and modifications required to apply the scheme to real-world flow problems. It allows the readers to understand and develop robust and efficient computer simulation models that can be used to model flow, contaminant transport, and other factors in rivers and coastal environments. The book includes a large set of tests to illustrate the use of the model for a wide range of applications.
Author: Dale R. Durran Publisher: Springer Science & Business Media ISBN: 1441964126 Category : Mathematics Languages : en Pages : 527
Book Description
This scholarly text provides an introduction to the numerical methods used to model partial differential equations, with focus on atmospheric and oceanic flows. The book covers both the essentials of building a numerical model and the more sophisticated techniques that are now available. Finite difference methods, spectral methods, finite element method, flux-corrected methods and TVC schemes are all discussed. Throughout, the author keeps to a middle ground between the theorem-proof formalism of a mathematical text and the highly empirical approach found in some engineering publications. The book establishes a concrete link between theory and practice using an extensive range of test problems to illustrate the theoretically derived properties of various methods. From the reviews: "...the books unquestionable advantage is the clarity and simplicity in presenting virtually all basic ideas and methods of numerical analysis currently actively used in geophysical fluid dynamics." Physics of Atmosphere and Ocean
Author: W. L. Wood Publisher: Oxford University Press ISBN: 9780198596905 Category : Mathematics Languages : en Pages : 290
Book Description
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: C.B. Vreugdenhil
Author: C.B. Vreugdenhil
Author: W.Y. Tan
Author: Jian Guo Zhou
Author: Gerhard H. Jirka
Author: Gayaz Khakimzyanov
Author: F. W. Wubs
Author: Abdul A. Khan
Author: Dale R. Durran
Author: G. S. Stelling
Author: W. L. Wood