An efficient algorithm for weakly compressible flows in spherical geometries

In this article, we present a direction splitting method, combined with a nonlinear iteration, for the compressible Navier-Stokes equations in spherical coordinates. The method is aimed at solving the equations on the sphere, and can be used for a regional geophysical simulations as well as simulations on the entire sphere. The aim of this work was to develop a method that would work efficiently in the limit of very small to vanishing Mach numbers, and we demonstrate here, using a numerical example, that the method shows good convergence and stability at Mach numbers in the range [10(-2), 10(-6)]. We also demonstrate the effect of some of the parameters of the model on the solution, on a common geophysical test case of a rising thermal bubble. The algorithm is particularly suitable for a massive parallel implementation, and we show below some results demonstrating its excellent weak scalability.

Automated summary

This article introduces a direction splitting method combined with a nonlinear iteration for compressible Navier-Stokes equations in spherical coordinates, suitable for simulations on the sphere or entire sphere. The method demonstrates good convergence and stability in the range of Mach numbers [10(-2), 10(-6)], with parameters affecting the solution shown in a geophysical test case. The algorithm is well-suited for massive parallel implementation, as demonstrated by excellent weak scalability results.