An upwind-biased conservative advection scheme for spherical hexagonal-pentagonal grids

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.