Computational Aspects of a Time Evolution Scheme for Incompressible Boussinesq Navier-Stokes in a Cylinder

Abstract

In this work we show some computational aspects of the implementation of a three dimensional spectral time evolution scheme for incompressible Boussinesq Navier-Stokes including rotation effects in a cylinder with a primitive variable formulation. The scheme is a second-order time-splitting method combined with pseudo-spectral Fourier Chebyshev in space. To deal with the singularity at the origin a radial expansion is considered in the diameter of the cylinder. The order expansion in the radial coordinate gets doubled. We develop a matrix processing that combines the use of the parity of the fields and the discretization functions to cancel half of the terms in the matrix reducing the radial dimension to the original one.