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A multi‐moment transport model on cubed‐sphere grid
Author(s) -
Chen C. G.,
Xiao F.,
Li X. L.,
Yang Y.
Publication year - 2010
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.2478
Subject(s) - moment (physics) , mathematics , finite volume method , grid , interpolation (computer graphics) , mathematical analysis , boundary (topology) , geometry , regular grid , benchmark (surveying) , mathematical optimization , classical mechanics , physics , mechanics , geography , motion (physics) , geodesy
A conservative, single‐cell‐based semi‐Lagrangian transport model is proposed in this paper. Using multi‐moment concept, an additional moment, i.e. volume‐integrated average (VIA), is treated as the model variable besides the point value (PV) updated in the traditional semi‐Lagrangian schemes. A quadratic interpolation function is constructed based on local degrees of freedom defined within each single cell. The PV moment is advanced by the semi‐Lagrangian formulation, whereas the VIA moment is updated by a finite volume formulation to rigorously ensure the numerical conservation. The numerical fluxes are computed from the PV moments defined along the boundary edges of the control volume. The scheme is extended to the spherical geometry through the application of the cubed‐sphere grid that eliminates the polar singularity in the conventional longitude/latitude coordinates by using the quasi‐uniform grid spacing covering the whole sphere. The single‐cell‐based scheme is well suited for the treatment of the connections between different patches. A simple quasi‐monotone limiter to the PV moment is applied to suppress non‐physical oscillations. The proposed scheme has been validated via representative benchmark tests and the performance is competitive to other existing transport schemes. Copyright © 2010 John Wiley & Sons, Ltd.