pizza: An open-source pseudo-spectral code for spherical quasi-geostrophic convection. (arXiv:1902.07092v1 [physics.flu-dyn])
<a href="http://arxiv.org/find/physics/1/au:+Gastine_T/0/1/0/all/0/1">T. Gastine</a>
We present a new pseudo-spectral open-source code nicknamed pizza. It is
dedicated to the study of rapidly-rotating Boussinesq convection under the 2-D
spherical quasi-geostrophic approximation, a physical hypothesis that is
appropriate to model the turbulent convection that develops in planetary
interiors. The code uses a Fourier decomposition in the azimuthal direction and
supports both a Chebyshev collocation method and a sparse Chebyshev integration
formulation in the cylindrically-radial direction. It supports several temporal
discretisation schemes encompassing multi-step time steppers as well as
diagonally-implicit Runge-Kutta schemes. The code has been tested and validated
by comparing weakly-nonlinear convection with the eigenmodes from a linear
solver. The comparison of the two radial discretisation schemes has revealed
the superiority of the Chebyshev integration method over the classical
collocation approach both in terms of memory requirements and operation counts.
The good parallelisation efficiency enables the computation of large problem
sizes with $mathcal{O}(10^4times 10^4)$ grid points using several thousands
of ranks. This allows the computation of numerical models in the turbulent
regime of quasi-geostrophic convection characterised by large Reynolds $Re$ and
yet small Rossby numbers $Ro$. A preliminary result obtained for a strongly
supercritical numerical model with a small Ekman number of $10^{-9}$ and a
Prandtl number of unity yields $Resimeq 10^5$ and $Ro simeq 10^{-4}$. pizza
is hence an efficient tool to study spherical quasi-geostrophic convection in a
parameter regime inaccessible to current global 3-D spherical shell models.
We present a new pseudo-spectral open-source code nicknamed pizza. It is
dedicated to the study of rapidly-rotating Boussinesq convection under the 2-D
spherical quasi-geostrophic approximation, a physical hypothesis that is
appropriate to model the turbulent convection that develops in planetary
interiors. The code uses a Fourier decomposition in the azimuthal direction and
supports both a Chebyshev collocation method and a sparse Chebyshev integration
formulation in the cylindrically-radial direction. It supports several temporal
discretisation schemes encompassing multi-step time steppers as well as
diagonally-implicit Runge-Kutta schemes. The code has been tested and validated
by comparing weakly-nonlinear convection with the eigenmodes from a linear
solver. The comparison of the two radial discretisation schemes has revealed
the superiority of the Chebyshev integration method over the classical
collocation approach both in terms of memory requirements and operation counts.
The good parallelisation efficiency enables the computation of large problem
sizes with $mathcal{O}(10^4times 10^4)$ grid points using several thousands
of ranks. This allows the computation of numerical models in the turbulent
regime of quasi-geostrophic convection characterised by large Reynolds $Re$ and
yet small Rossby numbers $Ro$. A preliminary result obtained for a strongly
supercritical numerical model with a small Ekman number of $10^{-9}$ and a
Prandtl number of unity yields $Resimeq 10^5$ and $Ro simeq 10^{-4}$. pizza
is hence an efficient tool to study spherical quasi-geostrophic convection in a
parameter regime inaccessible to current global 3-D spherical shell models.
http://arxiv.org/icons/sfx.gif
