  This paper introduces a formally second-order direction-splitting method for
solving the incompressible Navier-Stokes-Boussinesq system in a spherical shell
region. The equations are solved on overset Yin-Yang grids, combined with
spherical coordinate transforms. This approach allows to avoid the
singularities at the poles and keeps the grid size relatively uniform. The
downside is that the spherical shell is subdivided into two equally sized,
overlapping subdomains that requires the use of Schwarz-type iterations. The
temporal second order accuracy is achieved via an Artificial Compressibility
(AC) scheme with bootstrapping. The spatial discretization is based on second
order finite differences on the Marker-And-Cell (MAC) stencil. The entire
scheme is implemented in parallel using a domain decomposition iteration, and a
direction splitting approach for the local solves. The stability, accuracy and
weak scalability of the method is verified on a manufactured solution of the
Navier-Stokes-Boussinesq system and on the Landau solution of the Navier-Stokes
equations on the sphere.
