On the shallow atmosphere approximation in finite element dynamical cores
File(s)
Working paper
Author(s)
Cotter, CJ
Ham, DA
McRae, ATT
Mitchell, L
Natale, A
Type
Report
Abstract
We provide an approach to implementing the shallow atmosphere approximation in three dimensional finite element discretisations for dynamical cores. The approach makes use of the fact that the shallow atmosphere approximation metric can be obtained by writing equations on a three-dimensional manifold embedded in $mathbb{R}^4$ with a restriction of the Euclidean metric. We show that finite element discretisations constructed this way are equivalent to the use of a modified three dimensional mesh for the construction of metric terms. We demonstrate our approach via a convergence test for a prototypical elliptic problem.
Date Issued
2014-10-12
2015-04-17T14:42:19Z
Copyright Statement
© 2014 The Authors
Description
16.04.15 KB. Ok to add working paper to spiral, authors retain copyright
Identifier
http://arxiv.org/abs/1410.3069v1
Notes
Distributing this version for comments before submission