Luan F. Santos, Jeferson B. Granjeiro, Pedro S. Peixoto
Spherical centroidal Voronoi tessellations (SCVTs), currently used in numerical weather forecasting models such as the Model for Prediction Across Scales (MPAS), are a type of spherical grid that is highly flexible, allowing the construction of locally refined regions with higher resolution without requiring modifications to the numerical discretization or its implementation. However, the irregularity of SCVT grids makes the construction of robust high-order schemes challenging. In particular, in atmospheric modeling, high-order advection schemes are desirable since they reduce numerical diffusion and improve the representation of fine-scale tracer structures. Therefore, in this work, we propose a new class of high-order advection schemes on the sphere based on the $k$-exact reconstruction approach, extending their successful use on planar domains to the spherical surface. We assess the performance of the proposed method and compare it with existing advection schemes for SCVT grids used in MPAS. The evaluation includes classical advection test cases on the sphere as well as simulations with a mimetic finite-volume moist shallow-water model, in which the advection scheme is applied to the transport of moisture tracers. Grid-related robustness was investigated using locally refined spherical grids with a local focus on the Andes topography. Our results show that the proposed schemes achieve high-order accuracy in the advection tests, exhibit little sensitivity to grid distortion, and produce comparable results to existing schemes in the moist shallow-water model. Overall, grid robustness is therefore limited to the sensitivity of the discretization of the shallow-water model, irrespective of the advection scheme.