Linked e-resources
Details
Table of 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
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
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
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