𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Cubic Spline Collocation Method for the Shallow Water Equations on the Sphere

✍ Scribed by Anita T. Layton

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
140 KB
Volume
179
Category
Article
ISSN
0021-9991

No coin nor oath required. For personal study only.

✦ Synopsis

Spatial discretization schemes commonly used in global meteorological applications are currently limited to spectral methods or low-order finite-difference/finiteelement methods. The spectral transform method, which yields high-order approximations, requires Legendre transforms, which have a computational complexity of O(N 3 ), where N is the number of subintervals in one dimension. Thus, high-order finite-element methods may be a viable alternative to spectral methods. In this study, we present a new numerical method for solving the shallow water equations (SWE) in spherical coordinates. In this implementation, the SWE are discretized in time with the semi-implicit leapfrog method, and in space with the cubic spline collocation method on a skipped latitude-longitude grid. Numerical results for the Williamson

πŸ“œ SIMILAR VOLUMES

A Spline Collocation Scheme for the Sphe
A Spline Collocation Scheme for the Spherical Shallow Water Equations
✍ Jochen GΓΆttelmann πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 131 KB

The shallow water equations describe large scale horizontal phenomena of the global atmospheric motion to good approximation. Thus they provide a widely accepted primary test for numerical methods for global atmospheric modelling before proceeding to complete 3D baroclinic models [7]. They are progn