| Description |
1 online resource (328 p.) |
| Series |
Springer Atmospheric Sciences |
|
Springer atmospheric sciences.
|
| Contents |
Intro -- Foreword -- Preface -- Acknowledgments -- Contents -- Acronyms -- Introduction -- Numerics -- Discretization on Spherical Grids -- Efficiency of the Computational Grid -- Numerical Methods -- Validations of Numerical Methods Using NWP Models -- Verifications of Numerical Methods for Climate Modeling -- Simple Finite Difference Procedures -- The Runge-Kutta and Other Time Discretization Schemes -- Homogeneous and Inhomogeneous Difference Schemes -- Some Further Properties of Finite Difference Schemes -- The Von Neumann Method of Stability Analysis -- Dynamic Equations of Toy Models |
|
Diffusion -- The Boussinesq Model of Convection Between Heated Plates -- The Lorenz Paradigmatic Model -- Local-Galerkin Schemes in 1D -- Functional Representations, Amplitudes, and Basis Functions -- The Classic Galerkin Procedure -- Spectral Elements -- The L-Galerkin Scheme: o3o3 -- The L-Galerkin Scheme: o2o3 -- Splines of High Smoothness -- A Conserving Second-Order Scheme Using a Homogeneous FD Scheme -- Boundaries and Diffusion -- Transfer Function Analysis -- A Numerical Test for Irregular Resolution -- Internal Boundaries for Vertical Discretization -- Open Boundary Condition |
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The L-Galerkin scheme: o3o5C1C2 -- The L-Galerkin Scheme: o4o5C1C2 -- The Interface to Physics in High-Order L-Galerkin Schemes -- Polygonal Spline Solutions Using Distributions and Discontinuities -- Von Neumann Analysis of Some onom Schemes -- 2D Basis Functions for Triangular and Rectangular Meshes -- Rhomboidal Basis Functions and Sparse Grids for the Regular Grid Case -- Euclid's Lemma -- Triangular Basis Functions and Full Grids -- Triangular Basis Functions for the Rectangular Case -- The Corner Derivative Representation -- An Irregular Structured Quadrilateral Grid with Triangular Cells |
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An Example of a Regularization Operator -- Finite Difference Schemes on Sparse and Full Grids -- Non-conserving Schemes for Full Grids -- Alternative Methods to Compute Derivatives -- Baumgardner's Cloud Derivative Method -- Third-Order Differencing for Corner Points with a Second-Degree Polynomial Representation -- Enhanced Stencil Order -- The Full Triangular o3o3 Method -- Sparse Grids -- L-Galerkin Schemes for Sparse Triangular Meshes -- Totally Irregular Triangular and Quadrilateral Mesh: Hexagons and Other Polygons -- Staggered Grid Systems and Their Basis Function Representation |
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A Simple Cut-Cell System Based on the Staggered Low-Order Basis Functions -- A Conserving Version of the Cut-Cell Scheme -- Full and Sparse Hexagonal Grids in the Plane -- Indices and Basis Functions of Hexagonal Grids in a Plane -- Numerical Methods of Hexagonal Grids on the Plane -- Hexagonal Options -- Isotropy of the Hexagonal Grid in Comparison to Rhomboidal Grid -- Platonic and Semi-Platonic Solids -- Cubed Sphere, Icosahedron, and Examples of Semi-Platonic Solids -- Geometric Properties of Spherical Grids |
| Summary |
"Mathematics of the Weather" details the mathematical techniques used to create numerical models of the atmosphere. It explains methods which are currently considered for practical use in models for the exaflop computers (10**19 operations per seconds). This book is a guide to developing and modifying the mathematical methods used in such models. This includes Implementations in spherical geometry. The books also concentrates on elements of Numerical Weather Predication (NWP) and Computational Fluid Dynamics (CFD). |
| Notes |
Equations of Motion on the Spherical Grid and Non-conserving Finite Difference Schemes |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Online resource; title from PDF title page (SpringerLink, viewed November 2, 2022) |
| Subject |
Atmospheric models -- Mathematics
|
|
Meteorología -- Modelos matemáticos
|
|
Physical geography
|
|
Mathematics
|
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Physics
|
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Models matemàtics.
|
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Geografia física.
|
| Genre/Form |
Llibres electrònics.
|
| Form |
Electronic book
|
| Author |
Li, Jinxi
|
| ISBN |
9783031072383 |
|
3031072383 |
|
9788303107237 |
|
8303107232 |
|
