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

In this paper, 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 maximum 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.