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steppeler j mathematics weather methods spheres 2022

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Textbook in PDF format "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). Foreword Acronyms 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 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 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 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 Equations of Motion on the Spherical Grid and Non-conserving Finite Difference Schemes Further Spherical Test Problems Conserving L-Galerkin Schemes on the Sphere A Simple Non-conserving Homogeneous Order Discretization on the Sphere Hexagonal Grids on the Sphere Numerical Tests 1D Homogeneous Advection Test for onom Methods, SEM2 and SEM3 A Numerical Example of Open Boundary Condition for a Fast Wave The T64 Solid for Discretization by Quadrilateral Cells Shallow Water Tests on the Sphere: Solid Body Rotation, Solid Body Flow, Advection, and Williamson Test No. 6 2D Mountain Wave Test The Kalman Filter Data Analysis Test of the o3o3 Scheme on the Cubed Sphere Grid Using the Shallow Water Version of the HOMME Model Projections of Semi-platonic Solids to Triangular Surfaces CPU Time Used with a 3D Version of o3o3 Scheme 1D Example for the QUASAR System Operations of Linear Spaces Summary and Outlook Computer Aspects of Parallel Processing Numerical Weather Prediction for Small Research Groups and Owners of Private PCs New Applications for NWP Large Eddy Simulation The Elliptical and the Potato Shaped Earth Data Assimilation Global Models for Forecasting and Climate Research Linear Algebra Examples of Program Dispersion Analysis of o2o3 and o3o3 Methods 1D Homogeneous Advection Test Appendix A Neighborhood Relations for the Full Triangular Grid and a Compact Storage System The Serendipity Interpolation on the Sphere The Quasi-arithmetic Rendition QUASAR to Obtain a Sparse Field Representation

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Steppeler J. Mathematics of the Weather...Methods on Spheres 2022.pdf 7.6 MB

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steppeler j mathematics weather methods spheres 2022