Download or read book Efficient Numerical Methods for the Shallow Water Equations on the Sphere written by William Sawyer and published by . This book was released on 2006 with total page 123 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 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 the Shallow Water Equations written by Andreas Bollermann and published by . This book was released on 2011 with total page 154 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 130 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Standard Test Set for Numerical Approximations to the Shallow Water Equations in Spherical Geometry written by and published by . This book was released on 1991 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: A suite of seven test cases is proposed for the evaluation of numerical methods intended for the solution of the shallow water equations in spherical geometry. The shallow water equations exhibit the major difficulties associated with the horizontal dynamical aspects of atmospheric modeling on the spherical earth. These cases are designed for use in the evaluation of numerical methods proposed for climate modeling and to identify the potential trade-offs which must always be made in numerical modeling. Before a proposed scheme is applied to a full baroclinic atmospheric model it must perform well on these problems in comparison with other currently accepted numerical methods. The cases are presented in order of complexity. They consist of advection across the poles, steady state geostrophically balanced flow of both global and local scales, forced nonlinear advection of an isolated low, zonal flow impinging on an isolated mountain, Rossby-Haurwitz waves and observed atmospheric states. One of the cases is also identified as a computer performance/algorithm efficiency benchmark for assessing the performance of algorithms adapted to massively parallel computers. 31 refs.

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 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 Numerical Methods for the Three dimensional Shallow Water Equations on Supercomputers written by E. D. de Goede and published by . This book was released on 1993 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: Holl. Zusammenfass.

Download or read book An Efficient Numerical Scheme for the Two dimensional Shallow Water Equations Using Arithmetic Averaging written by P. Glaister and published by . This book was released on 1993 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Analysis of the Numerical Solution of the Shallow Water Equations written by Thomas A. Hamrick and published by . This book was released on 1997-09-01 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis is concerned with the analysis of various methods for the numerical solution of the shallow water equations along with the stability of these methods. Most of the thesis is concerned with the background and formaulation of the shallow water equations. The derivation of the basic equations will be given, in the primative variable and vorticity divergence formulation. Also the shallow water equations will be written in spherical coordinates. Two main types of methods used in approximating differential equations of this nature will be discussed. The two schemes are finite difference method (FDM) and the finite element method (FEM). After presenting the shallow water equations in several formulations, some examples will be presented. The use of the Fourier transform to find the solution of a semidiscrete analog of the shallow water equations is also demonstrated.

Download or read book A Shooting Method for the Solution of a Discrete Poisson Equation on the Surface of a Sphere written by Samuel Y. K. Yee and published by . This book was released on 1976 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: The solution of the Poisson equation plays an important role in problems such as air pollution and numerical weather prediction in geophysics and in problems such as fission in reactor physics. In the case of numerical weather prediction where solutions to the Poisson equation are required in daily routine operations, it is paramount that the solution procedure be efficient. An efficient shooting method is presented for the numerical solution of a discrete Poisson equation on the surface of the sphere. The solution is computed via two-dimensional shooting in the physical domain while the 'missing initial conditions' needed to start the shooting are obtained in a one-dimensional setting in the Fourier domain.

Download or read book High order Spatial Discretization Methods for the Shallow Water Equations written by Anita W. Tam and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We present new numerical methods for the shallow water equations on a sphere in spherical coordinates. In our implementation, the equations are discretized in time with the two-level semi-Lagrangian semi-implicit (SLSI) method, and in space on a staggered grid with the quadratic spline Galerkin (QSG) and the optimal quadratic spline collocation (OQSC) methods. When discretized on a uniform spatial grid, the solutions are shown through numerical experiments to be fourth-order in space locally at the nodes and midpoints of the spatial grids, and third-order globally. We also show that, when applied to a simplified version of the shallow water equations, each of our algorithms yields a neutrally stable solution for the meteorologically significant Rossby waves. Moreover, we demonstrate that the Helmholtz equation associated with the shallow water equations should be derived algebraically rather than analytically in order for the algorithms to be stable with respect to the Rossby waves. These results are verified numerically using Boyd's equatorial wave equations with initial conditions to generate a soliton. We then analyze the performance of our methods on various staggered grids--the A-, B-, and C-grids. From an eigenvalue analysis of our simplified version of the shallow water equations, we conclude that, when discretized on the C-grid, our algorithms faithfully capture the group velocity of inertia-gravity waves. Our analysis suggests that neither the A- nor B-grids will produce such good results. Our theoretical results are supported by numerical experiments, in which we discretize Boyd's equatorial wave equations using different staggered grids and set the initial conditions for the problem to generate gravitation modes instead of a soliton. With both the A- and B-grids, some waves are observed to travel in the wrong direction, whereas, with the C-grid, gravity waves of all wavelengths propagate in the correct direction.

Download or read book Numerical Methods for Shallow Water Equations written by Andrew Yershov and published by . This book was released on 1998 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Numerical Methods for the 3D Shallow Water Equations on Vector and Parallel Computers written by Erik D. de Goede and published by . This book was released on 1991 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: The performance of both iteration methods is accelerated by a technique based on smoothing. Both explicit and implicit smoothing is examined. It turns out that the unconditionally stable method is more efficient than the conditionally stable methods."

Download or read book Numerical Methods for Fluid Dynamics written by Dale R. Durran and published by Springer Science & Business Media. This book was released on 2010-09-14 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book The Taylor Galerkin Method for the Shallow Water Equations on the Sphere written by A. Priestley and published by . This book was released on 1991 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt: