We are currently working to build a non-hydrostatic model of the global atmosphere in the HOMME framework.
There are many ways to mesh the surface of the Earth (for use in a global atmospheric circulation model.) The latitude-longitude grid is probably the simplest and certainly the most familiar mesh, but it has problems. Near both the north and south poles, it exhibits coordinate singularities, and the meridians converge, producing grid-cells that get very small relative to those at the equator. (That's bad for explicit time stepping schemes, as it imposes a very small time step on the simulation.)
However the lat-long grid has some nice properties too: the coordinates are orthogonal (lines of latitude and longitude meet at right angles everywhere) and it is nearly uniform at low latitudes (near the equator.) So some people have investigated placing two overlapping sections of the lat-lon grid at right angles to each other, forming a new grid called the Yin-Yang grid. This is a composite, overset, or "chimera" grid, which is composed of sections, requiring interpolation when data passes from one section to the other. For high-order finite-difference solvers and finite-volume solvers, the data interpolation can be challenging. But for the Discontinuous-Galerking (DG) finite-element method, the interpolation is local, accurate, and simple.
It turns out the combination of DG and the Yin-Yang grid works remarkably well, at least for the various advection tests we have applied to it so far. For more details see our forthcoming publication:Discontinuous Transport on the Spherical Yin-Yang Overset Mesh.
Discontinuous-Galerkin Finite-Element solvers for atmospheric and ocean dynamics. (NCAR, IMAGe math institute)
Fluid-structure interaction for biologics and micro-air-vehicles (CU Boulder, Dept. Aerospace Eng.)
Fluid dynamics in automotive applications (Exa Corporation)
Fluid dynamics in micro-eletro-mechanical systems (MEMs) (Coventor Inc.)
Dynamics of molten block-copolymers and nano-composites (UCSB & Los Alamos National Lab)
Dynamics of white-dwarf stars (UCSB)
Remote Sensing for autonomous image-orthorectification and image-registration (Harris Corporation)
Optical Cooling of Semiconductors (CU Boulder, Dept. Physics)
High-Temperature Superconductivity (CU Boulder, Dept. Physics)