On the monotonic and conservative transport on overset/Yin–Yang grids

In this paper, we outline a simple and a general methodology to achieve positivity, monotonicity and mass conservation with transport schemes on general overset grids. The main feature of the approach is its reduced complexity, which simplifies the use of higher-order schemes and higher dimensions on general grids and in particular for overset grids. The method also does not degrade substantially the order of the overall scheme despite the extra constraints of monotonicity and conservation. The approach is applied to achieve mass conservation with semi-Lagrangian schemes and its performance is analyzed using simple one-dimensional overlapping grids and a two-dimensional spherical Yin–Yang grid. The Yin–Yang grid is a special overset grid for the sphere and it is of a special interest in the atmospheric modeling community, as it is one of the grids that may resolve the scaling issue of existing longitude–latitude-grid based atmospheric models on massively parallel machines.