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

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 reproduced the emission comparable to observations, one has to use realistic values for the Spitzer heat conductivity, which puts a large constrain on the time step of these simulations and therefore make them 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 constrain of the Alfv'en speed and speed up the simulations even further. We discuss the implementation of these two methods to the \PC 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. We find that with the use of the non-Fourier description of the heat flux evolution and the Boris correction, we can increase the time step of the simulation significantly without moving far away from the reference solution. However, for too low values of the Alfv'en speed limit, the simulation moves away from the reference solution und produces much higher temperatures and stronger emission structures.