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A positivity-preserving conservative semi-Lagrangian transport model bymulti-moment finite volume method has been developed on the cubed-sphere grid.In this paper, two kinds of moments, i.e. point values (PV moment) at cellboundaries and volume integrated average (VIA) value, are defined within asingle cell. The PV moment is updated by a conventional semi-Lagrangian method,while the VIA moment is cast by the flux form formulation that assures theexact numerical conservation. Different from the spatial approximation used inCSL2 (conservative semi-Lagrangian scheme with second order polynomialfunction) scheme, a monotonic rational function which can effectively removenon-physical oscillations and preserve the shape, is reconstructed in a singlecell by the PV moment and VIA moment. The resulting scheme is inherentlyconservative and can allow a CFL number larger than one. Moreover, the schemeuses only one cell for spatial reconstruction, which is very easy for practicalimplementation. The proposed model is evaluated by several widely usedbenchmark tests on cubed-sphere geometry. Numerical results show that theproposed transport model can effectively remove unphysical oscillationscompared with the CSL2 scheme and preserve the numerical non-negativity, and ithas the potential to transport the tracers accurately in real atmosphericmodel.

A positivity-preserving conservative Semi-Lagrangian Multi-moment Global Transport Model on the Cubed Sphere