Download or read book Multidimensional Upwind Schemes for the Shallow Water Equations written by H. Paillère and published by . This book was released on 1998 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Upwind Schemes for the Two dimensional Shallow Water Equations with Variable Depth Using Unstructured Meshes written by A. Bermùdez and published by . This book was released on 1995 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Genuinely Multidimensional High resolution Scheme for the Shallow water Equations written by Anne-Thérèse Morel and published by . This book was released on 1997 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Balanced Central Schemes for the Shallow Water Equations on Unstructured Grids written by Nasa Technical Reports Server (Ntrs) and published by BiblioGov. This book was released on 2013-08 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present a two-dimensional, well-balanced, central-upwind scheme for approximating solutions of the shallow water equations in the presence of a stationary bottom topography on triangular meshes. Our starting point is the recent central scheme of Kurganov and Petrova (KP) for approximating solutions of conservation laws on triangular meshes. In order to extend this scheme from systems of conservation laws to systems of balance laws one has to find an appropriate discretization of the source terms. We first show that for general triangulations there is no discretization of the source terms that corresponds to a well-balanced form of the KP scheme. We then derive a new variant of a central scheme that can be balanced on triangular meshes. We note in passing that it is straightforward to extend the KP scheme to general unstructured conformal meshes. This extension allows us to recover our previous well-balanced scheme on Cartesian grids. We conclude with several simulations, verifying the second-order accuracy of our scheme as well as its well-balanced properties.
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 An Adaptive Well Balanced Positivity Preserving Central Upwind Scheme for the Shallow Water Equations Over Quadtree Grids written by Seyed Mohammad Ali Ghazizadeh Fard and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Shallow water equations are widely used to model water flows in the field of hydrodynamics and civil engineering. They are complex, and except for some simplified cases, no analytical solution exists for them. Therefore, the partial differential equations of the shallow water system have been the subject of various numerical analyses and studies in past decades. In this study, we construct a stable and robust finite volume scheme for the shallow water equations over quadtree grids. Quadtree grids are two-dimensional semi-structured Cartesian grids that have different applications in several fields of engineering, such as computational fluid dynamics. Quadtree grids refine or coarsen where it is required in the computational domain, which gives the advantage of reducing the computational cost in some problems. Numerical schemes on quadtree grids have different properties. An accurate and robust numerical scheme is able to provide a balance between the flux and source terms, preserve the positivity of the water height and water surface, and is capable of regenerating the grid with respect to different conditions of the problem and computed solution. The proposed scheme uses a piecewise constant approximation and employs a high-order Runge-Kutta method to be able to make the solution high-order in space and time. Hence, in this thesis, we develop an adaptive well-balanced positivity preserving scheme for the shallow water system over quadtree grids utilizing different techniques. We demonstrate the formulations of the proposed scheme over one of the different configurations of quadtree cells. Six numerical benchmark tests confirm the ability of the scheme to accurately solve the problems and to capture small perturbations. Furthermore, we extend the proposed scheme to the coupled variable density shallow water flows and establish an extended method where we focus on eliminating nonphysical oscillations, as well as well-balanced, positivity preserving, and adaptivity properties of the scheme. Four different numerical benchmark tests show that the proposed extension of the scheme is accurate, stable, and robust.
Download or read book Multidimensional Scheme for the Shallow Water Equations written by A.-T. Morel and published by . This book was released on 1996 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Water Waves The Mathematical Theory with Applications written by James Johnston Stoker and published by Courier Dover Publications. This book was released on 2019-04-17 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 1957, this is a classic monograph in the area of applied mathematics. It offers a connected account of the mathematical theory of wave motion in a liquid with a free surface and subjected to gravitational and other forces, together with applications to a wide variety of concrete physical problems. A never-surpassed text, it remains of permanent value to a wide range of scientists and engineers concerned with problems in fluid mechanics. The four-part treatment begins with a presentation of the derivation of the basic hydrodynamic theory for non-viscous incompressible fluids and a description of the two principal approximate theories that form the basis for the rest of the book. The second section centers on the approximate theory that results from small-amplitude wave motions. A consideration of problems involving waves in shallow water follows, and the text concludes with a selection of problems solved in terms of the exact theory. Despite the diversity of its topics, this text offers a unified, readable, and largely self-contained treatment.
Download or read book Godunov Methods written by E.F. Toro and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 1050 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited review book on Godunov methods contains 97 articles, all of which were presented at the international conference on Godunov Methods: Theory and Applications, held at Oxford in October 1999, to commemo rate the 70th birthday of the Russian mathematician Sergei K. Godunov. The meeting enjoyed the participation of 140 scientists from 20 countries; one of the participants commented: everyone is here, meaning that virtu ally everybody who had made a significant contribution to the general area of numerical methods for hyperbolic conservation laws, along the lines first proposed by Godunov in the fifties, was present at the meeting. Sadly, there were important absentees, who due to personal circumstance could not at tend this very exciting gathering. The central theme o{ the meeting, and of this book, was numerical methods for hyperbolic conservation laws fol lowing Godunov's key ideas contained in his celebrated paper of 1959. But Godunov's contributions to science are not restricted to Godunov's method.
Download or read book Conservative Multidimensional Upwinding for the Steady Two dimensional Shallow Water Equations written by M. E. Hubbard and published by . This book was released on 1997 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Conservative Multidimensional Upwinding for the Shallow Water Equations written by M. E. Hubbard and published by . This book was released on 1995 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Upwind Scheme for the 2D Shallow Water Equations with Applications written by P. Brufau and published by . This book was released on 1998 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Genuinely Multidimensional Upwinding for the 2D Shallow Water Equations written by P. Garcia-Navarro and published by . This book was released on 1994 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Well Balanced Central Scheme for the Two dimensional Shallow Water Equations written by Sarah Tarek Khankan and published by . This book was released on 2010 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: We aim to develop a new class of well-balanced non-oscillatory second-order accurate central schemes for the approximating solution of general two-dimensional hyperbolic systems, and in particular to approximate the solution of shallow water equation systems (SWE) on Cartesian grids. The base scheme evolves the numerical solution on a unique Cartesian grid and avoids the resolution of the Riemann problems arising at the cell interfaces thanks to a layer of ghost staggered cells implicitly used while updating the solution. --The system of shallow water equations represents a good mathematical model for the hydrodynamics of coastal oceans, simulation of flows in channels and rivers, study of large-scale waves and vertically averaged regimes in the atmosphere and ocean. Here h denotes the water depth, (u, v) represents the flow velocity, g is the gravitational constant, and b is the function that models the water bed topography. b vanishes in the case of a flat riverbed and the resulting system becomes a hyperbolic system. Most numerical schemes fail to maintain the steady state constraint of shallow water equation problems and generate numerical (nonphysical) waves and storms. In this project, we shall investigate several approaches that could be coupled with our numerical base scheme in order to ensure, when necessary, the steady state condition of SWE systems.
Download or read book Finite Volume Methods for Hyperbolic Problems written by Randall J. LeVeque and published by Cambridge University Press. This book was released on 2002-08-26 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, first published in 2002, contains an introduction to hyperbolic partial differential equations and a powerful class of numerical methods for approximating their solution, including both linear problems and nonlinear conservation laws. These equations describe a wide range of wave propagation and transport phenomena arising in nearly every scientific and engineering discipline. Several applications are described in a self-contained manner, along with much of the mathematical theory of hyperbolic problems. High-resolution versions of Godunov's method are developed, in which Riemann problems are solved to determine the local wave structure and limiters are then applied to eliminate numerical oscillations. These methods were originally designed to capture shock waves accurately, but are also useful tools for studying linear wave-propagation problems, particularly in heterogenous material. The methods studied are implemented in the CLAWPACK software package and source code for all the examples presented can be found on the web, along with animations of many of the simulations. This provides an excellent learning environment for understanding wave propagation phenomena and finite volume methods.
Download or read book Numerical Methods for Conservation Laws written by LEVEQUE and published by Birkhäuser. This book was released on 2013-11-11 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes developed from a course on the numerical solution of conservation laws first taught at the University of Washington in the fall of 1988 and then at ETH during the following spring. The overall emphasis is on studying the mathematical tools that are essential in de veloping, analyzing, and successfully using numerical methods for nonlinear systems of conservation laws, particularly for problems involving shock waves. A reasonable un derstanding of the mathematical structure of these equations and their solutions is first required, and Part I of these notes deals with this theory. Part II deals more directly with numerical methods, again with the emphasis on general tools that are of broad use. I have stressed the underlying ideas used in various classes of methods rather than present ing the most sophisticated methods in great detail. My aim was to provide a sufficient background that students could then approach the current research literature with the necessary tools and understanding. vVithout the wonders of TeX and LaTeX, these notes would never have been put together. The professional-looking results perhaps obscure the fact that these are indeed lecture notes. Some sections have been reworked several times by now, but others are still preliminary. I can only hope that the errors are not too blatant. Moreover, the breadth and depth of coverage was limited by the length of these courses, and some parts are rather sketchy.
