Paper Info
Title
A fourth-order numerical method for the planetary geostrophic equations with inviscid geostrophic balance
Abstract
The planetary geostrophic equations with inviscid balance equation are reformulated in an alternate form, and a fourth-order finite difference numerical method of solution is proposed and analyzed in this article. In the reformulation, there is only one prognostic equation for the temperature field and the velocity field is statically determined by the planetary geostrophic balance combined with the incompressibility condition. The key observation is that all the velocity profiles can be explicitly determined by the temperature gradient, by utilizing the special form of the Coriolis parameter. This brings convenience and efficiency in the numerical study. In the fourth-order scheme, the temperature is dynamically updated at the regular numerical grid by long-stencil approximation, along with a one-sided extrapolation near the boundary. The velocity variables are recovered by special solvers on the 3-D staggered grid. Furthermore, it is shown that the numerical velocity field is divergence-free at the discrete level in a suitable sense. Fourth order convergence is proven under mild regularity requirements.
Year
DOI
Venue
2007
10.1007/s00211-007-0104-z
Numerische Mathematik
Keywords
Field
DocType
numerical velocity field,numerical study,fourth-order numerical method,temperature field,numerical method,3-d staggered grid,planetary geostrophic equation,velocity variable,inviscid geostrophic balance,temperature gradient,velocity profile,regular numerical grid,velocity field,finite difference
Inviscid flow,Differential equation,Finite difference,Mathematical analysis,Geostrophic wind,Balance equation,Finite difference method,Numerical analysis,Finite volume method,Mathematics
Journal
Volume
Issue
ISSN
107
4
0945-3245
Citations 
PageRank 
References 
3
0.44
4
Authors
4
Name
Order
Citations
PageRank
Roger Samelson191.48
Roger Temam24412.47
Cheng Wang361.22
Shouhong Wang431542.45