Download or read book Time Integration of the Shallow Water Equations in Spherical Geometry written by D. Lanser and published by . This book was released on 2000 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Finite volume Discretization of the Shallow water Equations in Spherical Geometry written by Lars Pesch and published by . This book was released on 2002 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Spatial Discretization of the Shallow Water Equations in Spherical Geometry Using Osher Scheme written by D. Lanser and published by . This book was released on 1999 with total page 34 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 Numerical Solution of Time Dependent Advection Diffusion Reaction Equations written by Willem Hundsdorfer and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unique book on Reaction-Advection-Diffusion problems
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 Adaptive Atmospheric Modeling written by Jr̲n Behrens and published by Springer Science & Business Media. This book was released on 2006-08-11 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gives an overview and guidance in the development of adaptive techniques for atmospheric modeling. This book covers paradigms of adaptive techniques, such as error estimation and adaptation criteria. Considering applications, it demonstrates several techniques for discretizing relevant conservation laws from atmospheric modeling.
Download or read book Computational Techniques for Modeling Atmospheric Processes written by Prusov, Vitaliy and published by IGI Global. This book was released on 2017-06-16 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: Meteorology has made significant strides in recent years due to the development of new technologies. With the aid of the latest instruments, the analysis of atmospheric data can be optimized. Computational Techniques for Modeling Atmospheric Processes is an academic reference source that encompasses novel methods for the collection and study of meteorological data. Including a range of perspectives on pertinent topics such as air pollution, parameterization, and thermodynamics, this book is an ideal publication for researchers, academics, practitioners, and students interested in instrumental methods in the study of atmospheric processes.
Download or read book Cartesian Methods for the Shallow Water Equations on a Sphere written by and published by . This book was released on 2000 with total page 47 pages. Available in PDF, EPUB and Kindle. Book excerpt: The shallow water equations in a spherical geometry are solved using a 3-dimensional Cartesian method. Spatial discretization of the 2-dimensional, horizontal differential operators is based on the Cartesian form of the spherical harmonics and an icosahedral (spherical) grid. Computational velocities are expressed in Cartesian coordinates so that a problem with a singularity at the pole is avoided. Solution of auxiliary elliptic equations is also not necessary. A comparison is made between the standard form of the Cartesian equations and a rotational form using a standard set of test problems. Error measures and conservation properties of the method are reported for the test problems.
Download or read book A Vorticity Divergence Global Semi Lagrangian Spectral Model for the Shallow Water Equations written by and published by . This book was released on 2001 with total page 45 pages. Available in PDF, EPUB and Kindle. Book excerpt: The shallow water equations modeling flow on a sphere are useful for the development and testing of numerical algorithms for atmospheric climate and weather models. A new formulation of the shallow water equations is derived which exhibits an advective form for the vorticity and divergence. This form is particularly well suited for numerical computations using a semi-Lagrangian spectral discretization. A set of test problems, standard for the shallow water equations on a sphere, are solved and results compared with an Eulerian spectral model. The semi-Lagrangian transport method was introduced into atmospheric modeling by Robert, Henderson, and Turnbull. A formulation based on a three time level integration scheme in conjunction with a finite difference spatial discretization was studied by Ritchie. Two time level grid point schemes were derived by Bates et al. Staniforth and Cote survey developments of the application of semi-Lagrangian transport (SLT) methods for shallow water models and for numerical weather prediction. The spectral (or spherical harmonic transform) method when combined with a SLT method is particularly effective because it allows for long time steps avoiding the Courant-Friedrichs-Lewy (CFL) restriction of Eulerian methods, while retaining accurate (spectral) treatment of the spatial derivatives. A semi-implicit, semi-Lagrangian formulation with spectral spatial discretization is very effective because the Helmholz problem arising from the semi-implicit time integration can be solved cheaply in the course of the spherical harmonic transform. The combination of spectral, semi-Lagrangian transport with a semi-implicit time integration schemes was first proposed by Ritchie. A advective formulation using vorticity and divergence was introduced by Williamson and Olson. They introduce the vorticity and divergence after the application of the semi-Lagrangian discretization. The semi-Lagrangian formulation of Williamson and Olson and Bates et al. has the property that the metric terms of the advective form are treated discretely requiring a delicate spherical vector addition of terms at the departure point and arrival point. In their formulation, the metric terms associated with the advection operator do not appear explicitly. The spherical geometry associated with the combination of vector quantities at arrival and departure points treats the metric terms and is derived in Bates et al. The formulation derived in this paper avoids this vector addition. It is possible to do this because our formulation is based entirely on a scalar, advective form of the momentum equations. This new form is made possible by the generalization of a vector identity to spherical geometry. In Section 2 the standard form of the shallow water equations in spherical geometry are given. Section 3 presents the vector identities needed to derive an advective form of the vorticity and divergence equations. The semi-implicit time integration and semi-Lagrangian transport method are described in Section 4. The SLT interpolation scheme is described in Section 5. Section 6 completes the development of the discrete model with the description of the semi-implicit spectral equations. A discussion of results on several standard test problems is contained in Section 7.
Download or read book Computational Science Iccs 2005 written by V.S. Sunderam and published by Springer Science & Business Media. This book was released on 2005-05-12 with total page 1201 pages. Available in PDF, EPUB and Kindle. Book excerpt: The three-volume set LNCS 3514-3516 constitutes the refereed proceedings of the 5th International Conference on Computational Science, ICCS 2005, held in Atlanta, GA, USA in May 2005.The 464 papers presented were carefully reviewed and selected from a total of 834 submissions for the main conference and its 21 topical workshops. The papers span the whole range of computational science, ranging from numerical methods, algorithms, and computational kernels to programming environments, grids, networking, and tools. These fundamental contributions dealing with computer science methodologies and techniques are complemented by papers discussing computational applications and needs in virtually all scientific disciplines applying advanced computational methods and tools to achieve new discoveries with greater accuracy and speed.
Download or read book Fourier Analysis of Numerical Approximations of Hyperbolic Equations written by R. Vichnevetsky and published by SIAM. This book was released on 1982-01-01 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides useful reference material for those concerned with the use of Fourier analysis and computational fluid dynamics.
Download or read book A Comparison of Operator Splitting and Approximate Matrix Factorization for the Shallow Water Equations in Spherical Geometry written by D. Lanser and published by . This book was released on 2001 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 A Discontinuous Galerkin Method for the Shallow Water Equations in Spherical Triangular Coordinates written by and published by . This book was released on 2007 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: A global barotropic model of the atmosphere is presented governed by the shallow water equations and discretized by a Runge-Kutta discontinuous Galerkin method on an unstructured triangular grid. The shallow water equations on the sphere, a two-dimensional surface in R3, are locally represented in terms of spherical triangular coordinates, the appropriate local coordinate mappings on triangles. On every triangular grid element, this leads to a two-dimensional representation of tangential momentum and therefore only two discrete momentum equations. The discontinuous Galerkin method consists of an integral formulation using a Rusanov numerical flux. A strong stability-preserving third order Runge-Kutta method is applied for the time discretization. The polynomial space of order k on each curved triangle of the grid is characterized by a Lagrange basis and requires high-order quadature rules for the integration over elements and element faces. For the presented method no mass matrix inversion is necessary, except in a preprocessing step.
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 134 pages. Available in PDF, EPUB and Kindle. Book excerpt:
