Modeling the thermal conduction in the solar atmosphere with the code MANCHA3D

TL;DR

This paper introduces and validates two numerical schemes for modeling thermal conduction in the solar atmosphere within the MANCHA3D code, incorporating Braginskii's heat flux model and addressing computational efficiency.

Contribution

It implements and compares two heat conduction schemes in MANCHA3D, including a novel hyperbolic approach and a comprehensive Braginskii-based model for solar plasma.

Findings

Both schemes are validated with standard tests in multiple dimensions.

The hyperbolic scheme mitigates time step limitations of explicit parabolic methods.

The Braginskii model accounts for magnetic field effects on heat flux.

Abstract

Thermal conductivity is one of the important mechanisms of heat transfer in the solar corona. In the limit of strongly magnetized plasma, it is typically modeled by Spitzer's expression where the heat flux is aligned with the magnetic field. This paper describes the implementation of the heat conduction into the code MANCHA3D with an aim of extending single-fluid MHD simulations from the upper convection zone into the solar corona. Two different schemes to model heat conduction are implemented: (1) a standard scheme where a parabolic term is added to the energy equation, and (2) a scheme where the hyperbolic heat flux equation is solved. The first scheme limits the time step due to the explicit integration of a parabolic term, which makes the simulations computationally expensive. The second scheme solves the limitations on the time step by artificially limiting the heat conduction speed to computationally manageable values. The validation of both schemes is carried out with standard tests in one, two, and three spatial dimensions. Furthermore, we implement the model for heat flux derived by Braginskii (1965) in its most general form, when the expression for the heat flux depends on the ratio of the collisional to cyclotron frequencies of the plasma, and, therefore on the magnetic field strength. Additionally, our implementation takes into account the heat conduction in parallel, perpendicular, and transverse directions, and provides the contributions from ions and electrons separately. The model also transitions smoothly between field-aligned conductivity and isotropic conductivity for regions with a low or null magnetic field. Finally, we present a two-dimensional test for heat conduction using realistic values of the solar atmosphere where we prove the robustness of the two schemes implemented.