A Conservative Positive-Definite Multi-Moment Center-Constrained Finite Volume Transport Model on Cubed Sphere

In this study, the adaption of a novel three-point multi-moment constrained finite-volume transport scheme for uniform points with center constraints (MCV3_UPCC) to cubed sphere geometry is implemented and described. For the MCV3_UPCC scheme, the three equidistant solution points are located within a single cell and a polynomial of 4th degree can be built by imposing the multi-moment center constraints. The resultant scheme has third-order accuracy and guarantees the exact numerical conservation. The Fourier analysis of MCV3_UPCC scheme demonstrates that the novel MCV3_UPCC has better numerical dissipation and dispersion than the original 3rd order Multi-moment Constrained finite Volume (MCV3) scheme. Then it is applied to quasi-uniform cubed-sphere grid, which is designed to avoid the polar problem on the traditional latitude–longitude grid. To suppress the non-physical numerical oscillations, a bound-preserving (BP) algorithm to constrain the conserved advected tracer to within the initial maxi-mum and minimum values is also implemented. The scheme is validated with several widely used benchmarks involving prescribed non-divergent two-dimensional flow on the sphere and different initial tracer distributions. The resulting conservative transport model with high-order accuracy and positive preserving property is comparable to other high-order schemes and has the potential for the numerical simulation of various traces in the atmosphere.