2208 Conservative and accurate advection transport on sphere with the gnomonic cube grid

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A conservative and accurate scheme of advection transport is devised for the spherical geometry. The sphere is represented by the gnomonic cubic grid. The piecewise interpolation reconstruction of the transported field is built in terms of both the volume integrated average (VIA) and the point value (PV) of the field variable over each mesh element of quadrangle. In the present formulation, the VIA and the PV, which are generically called "moments", are defined over each control volume (i.e. the mesh element) and its boundary. The point values are predicted through a semi-Lagrangian solution, while the volume integrated values are updated by a finite volume formulation of flux form. A 2D quadratic polynomial is constructed over each mesh element, and a third-order scheme is obtained.

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