Driving solar coronal MHD simulations on high-performance computers

Abstract

The quality of today's research is often tightly limited to the available computing power and scalability of codes to many processors. For example, tackling the problem of heating the solar corona requires a most realistic description of the plasma dynamics and the magnetic field. Numerically solving such a magneto-hydrodynamical (MHD) description of a small active region (AR) on the Sun requires millions of computation hours on current high-performance computing (HPC) hardware. The aim of this work is to describe methods for an efficient parallelization of boundary conditions and data input/output (IO) strategies that allow for a better scaling towards thousands of processors (CPUs). The Pencil Code is tested before and after optimization to compare the performance and scalability of a coronal MHD model above an AR. We present a novel boundary condition for non-vertical magnetic fields in the photosphere, where we approach the realistic pressure increase below the photosphere. With that, magnetic flux bundles become narrower with depth and the flux density increases accordingly. The scalability is improved by more than one order of magnitude through the HPCfriendly boundary conditions and IO strategies. This work describes also the necessary nudging methods to drive the MHD model with observed magnetic fields from the Sun's photosphere. In addition, we present the upper and lower atmospheric boundary conditions (photospheric and towards the outer corona), including swamp layers to diminish perturbations before they reach the boundaries. Altogether, these methods enable more realistic 3D MHD simulations than previous models regarding the coronal heating problem above an AR -simply because of the ability to use a large amount of CPUs efficiently in parallel.

Numerical evidence for a small-scale dynamo approaching solar magnetic Prandtl numbers

“…We use the Pencil Code [44] to perform all simulations, with parallelized fast-Fourier-transforms to calculate the spectra on the fly [45]. Pencil Code is freely available under https://github.com/pencil-code/.…”

Successive injection of opposite magnetic helicity in solar active region NOAA 11928

“…A special driver module is developed to load the bottom boundary magnetic field observations and then feed the simulation as the time progresses in steps of integration time. We use a modification of the implementation by (Bingert & Peter 2011;Bourdin 2020;Warnecke & Bingert 2020). The time step δt is normally specified as Courant time step through the coefficients c δ t(= 0.9), c δt,v (= 0.25) as given by…”

The Pencil Code, a modular MPI code for partial differential equations and particles: multipurpose and multiuser-maintained

“…• Thermal instability and mixing (C.-C. Yang & Krumholz, 2012), • Implicit solver for temperature (Gastine & Dintrans, 2008), • Dust-gas dynamics with mutual drag interaction (C.-C. Yang & Johansen, 2016;), • Boundary conditions for the solar atmosphere and HDF5 format (Philippe-A. Bourdin, 2020).…”