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 .

agnetohydrodynamics , solar corona , Sun , magnetic fields , coronal heating