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The hot loop structures in the solar corona can be well modeled by threedimensional magnetohydrodynamic simulations, where the corona is heated byfield line braiding driven at the photosphere. To be able to reproduce theemission comparable to observations, one has to use realistic values for theSpitzer heat conductivity, which puts a large constraint on the time step ofthese simulations and make them therefore computationally expensive. Here, wepresent a non-Fourier description of the heat flux evolution, which allow us tospeed up the simulations significantly. Together with the semi-relativisticBoris correction, we are able to limit the time step constraint of the Alfv\'enspeed and speed up the simulations even further. We discuss the implementationof these two methods to the Pencil Code and present their implications on thetime step, and the temperature structures, the ohmic heating rate and theemission in simulations of the solar corona. Using a non-Fourier description ofthe heat flux evolution together with the Boris correction, we can increase thetime step of the simulation significantly without moving far away from thereference solution. However, for values of the Alfv\'en speed limit of 3 000km/s and below, the simulation moves away from the reference solution undproduces much higher temperatures and much structures with stronger emission.

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