A finite–difference scheme for three–dimensional incompressible flows in spherical coordinates

In this study we have developed a flexible and efficient numerical scheme for the simulation of three–dimensional incompressible flows in spherical coordinates. The main idea, inspired by similar strategy as [1] cylindrical coordinates, consists change variables combined with discretization on staggered mesh special treatment few discrete terms that remove singularities Navier–Stokes equations at sphere centre along polar axis. This new method alleviates also time step restrictions introduced around axis while it still suffers from strong limitations if convection dominates flow. is second–order accurate space verified validated computing examples are compared results produced other codes or available literature. can cope evolving whole sphere, shell sector without any and, thanks to flexibility finite–differences, employ generic stretching (in two three directions) complex boundary conditions.