Open AccessAn Upwind-Biased Conservative Advection Scheme for Spherical Hexagonal–Pentagonal Grids
Author(s) -
Hiroaki Miura
Publication year - 2007
Publication title -
monthly weather review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.862
H-Index - 179
eISSN - 1520-0493
pISSN - 0027-0644
DOI - 10.1175/2007mwr2101.1
Subject(s) - upwind scheme , mathematics , advection , piecewise linear function , mathematical analysis , numerical diffusion , geometry , discretization , physics , mechanics , thermodynamics
A discrete form of the flux-divergence operator is developed to compute advection of tracers on spherical hexagonal–pentagonal grids. An upwind-biased advection scheme based on a piecewise linear approximation for one-dimensional regular grids is extended simply for spherical hexagonal–pentagonal grids. The distribution of a tracer over the upwind side of a cell face is linearly approximated using a nodal value and a gradient at a computational node on the upwind side. A piecewise linear approximation is relaxed to a local linear approximation, and the relaxation precludes the complicated conditional branching present in remapping schemes. Results from a cosine bell advection test show that the new scheme compares favorably with other upwind-biased schemes for spherical hexagonal–pentagonal grids.