A high‐order multi‐moment constrained finite‐volume global shallow‐water model on the Yin‐Yang grid. (31st January 2015)

• Record Type: Journal Article
• Authors: Li, Xingliang; Chen, Chungang; Xiao, Feng; Shen, Xueshun
• Is Part Of: Quarterly journal of the Royal Meteorological Society. Volume 141:Number 691(2015:Jul.)
• Page Start: 2090
• Page End: 2102
• Publication Date: 2015-01-31
• Subjects: Meteorology -- Periodicals; 551.5
• DOI: 10.1002/qj.2504
• Languages: English
• ISSNs: 0035-9009

Abstract

<abstract abstract-type="main" id="qj2504-abs-0001"> <title> <x xml:space="preserve">Abstract</x> </title> <p id="qj2504-para-0001">A high‐order global shallow‐water model on a Yin‐Yang grid has been developed by using the multi‐moment constrained finite‐volume (MCV) method. Unlike the traditional finite‐volume method, more degrees of freedom (DOFs)–which are the values at the solution points within each mesh element–are defined and updated in time. The time evolution equations for these point values (PVs) are derived from a set of constraint conditions in terms of the so‐called multi‐moment quantities, such as the PV, the volume‐integrated average (VIA) and derivative. Different moments use different forms of equations which are all consistent with the shallow‐water equations, among which the VIA moment is computed from a finite‐volume formulation of flux form that guarantees rigorous numerical conservation. A fourth‐order formulation is devised with the third‐order reconstruction built over each element using the DOFs locally available. A simple and orthogonal overset grid, the Yin‐Yang grid, is used to represent the spherical geometry with quasi‐uniform grid spacing. The resulting global shallow‐water model is attractive in algorithmic simplicity and computational efficiency. The model has been validated by widely used benchmark tests. The numerical results of the present model are competitive with most existing advanced models.</p> </abstract>