Astronomy and Astrophysics
Aims: 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.
Methods: 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.
Results: 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, Reviews of Plasma Physics, 205) 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 recovers Spitzer's expression for parallel thermal conductivity in the strongly magnetized limit but also transitions smoothly between field-aligned conductivity and isotropic conductivity for regions with a low or null magnetic field. We describe the details of the implementation of Braginskii's thermal conductivity using a combination of the first scheme for the perpendicular and transverse directions and the second scheme for the parallel component. We estimate thermal conductivities in a quiet-Sun model. In this model, we find that the perpendicular and transverse components for electrons and ions and the parallel component for ions might have some significance below the transition region. Above the transition region only the parallel component for ions might be important. 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 and show that our adaptation of the hyperbolic treatment offers a great advantage over the computational cost of the simulations.
Numerical simulation through complex computer codes has been a fundamental tool in physics and technology research for decades. The rapid growth of computing capabilities, coupled with significant advances in numerical mathematics, has made this branch of research accessible to medium-sized research centers, bridging the gap between theoretical and
Magnetic fields are at the base of star formation and stellar structure and evolution. When stars are born, magnetic fields brake the rotation during the collapse of the mollecular cloud. In the end of the life of a star, magnetic fields can play a key role in the form of the strong winds that lead to the last stages of stellar evolution. During