Non-Fourier description of heat flux evolution in 3D MHD simulations of the solar corona

Abstract

The hot loop structures in the solar corona can be well modeled by three dimensional magnetohydrodynamic simulations, where the corona is heated by field line braiding driven at the photosphere. To be able to reproduce the emission comparable to observations, one has to use realistic values for the Spitzer heat conductivity, which puts a large constraint on the time step of these simulations and make them therefore computationally expensive. Here, we present a non-Fourier description of the heat flux evolution, which allow us to speed up the simulations significantly. Together with the semi-relativistic Boris correction, we are able to limit the time step constraint of the Alfvén speed and speed up the simulations even further. We discuss the implementation of these two methods to the Pencil Code and present their implications on the time step, and the temperature structures, the ohmic heating rate and the emission in simulations of the solar corona. Using a non-Fourier description of the heat flux evolution together with the Boris correction, we can increase the time step of the simulation significantly without moving far away from the reference solution. However, for values of the Alfvén speed limit of 3 000 km/s and below, the simulation moves away from the reference solution und produces much higher temperatures and much structures with stronger emission.

Stellar X-rays and magnetic activity in 3D MHD coronal models

“…( 14) by a nonFourier heat-flux scheme. See Warnecke & Bingert (2020) for a detailed description and discussion. Additionally, we use a semi-relativistic correction to the Lorentz force similar to the work of Boris (1970), Gombosi et al (2002) and Rempel (2017).…”

“…Additionally, we use a semi-relativistic correction to the Lorentz force similar to the work of Boris (1970), Gombosi et al (2002) and Rempel (2017). For details of the implementation, see Chatterjee (2020) and Warnecke & Bingert (2020).…”

“…This is a snapshot of the active region AR 11102 as observed with the Helioseismic and Magnetic Imager (HMI; Schou et al 2012) on August 30, 2010. A detailed description of a similar active region and how it is implemented in the model is discussed in Warnecke & Bingert (2020). These kinds of magnetograms represent a typical situation for a solar active region and similar magnetograms have been used as input for data-driven simulations in earlier studies (see e.g., Gudiksen & Nordlund 2005a,b;Bingert & Peter 2011).…”

Introduction

“…He also discusses the scalability of the code, with the introduction of the extendable HDF5 file format and input-output strategies that are better suited for modern supercomputers. Warnecke and Bingert (2020) further improved such a model of the solar corona by using the Boris correction implemented by Chatterjee (2020) and further characterise its properties in their work on non-Fickian or non-Fourier heat conduction using the telegraph equation. This approach is analogous to what was done previously to solve for cosmic ray diffusion in the interstellar medium (Snodin et al 2006) with a very large diffusion coefficient, which would severely limit the time step.…”

Modelling the corona of stars more active than the Sun using 3D MHD simulations

“…4). After the recent implementations of a non-Fourier heat flux scheme and the Boris correction (see Warnecke and Bingert 2020), a parameter study is now possible. We investigate the L X ∝ Φ m through a simple analytical model and a series of 3D MHD numerical experiments.…”