A direction splitting scheme for Navier–Stokes–Boussinesq system in spherical shell geometries

This article introduces a second-order direction splitting method for solving the incompressible Navier–Stokes–Boussinesq system in spherical shell region. The equations are solved on overset Yin–Yang grids, combined with coordinate transforms. approach allows to avoid singularities at poles and keeps grid size relatively uniform. downside is that subdivided into two equally sized, overlapping subdomains requires use of Schwarz-type iterations. temporal accuracy achieved via an artificial compressibility scheme bootstrapping. spatial discretization based finite differences Marker-And-Cell stencil. entire implemented parallel using domain decomposition iteration local solves. stability, accuracy, weak scalability verified manufactured solution while its practicality demonstrated natural convection problem gap between concentric spheres.