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 modelled 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 allows 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 Alfv?n 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 Alfv?n speed limit of 3000 and below, the simulation moves away from the reference solution and produces much higher temperatures and much structures with stronger emission.