ABSTRACT 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 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 3000 and below, the simulation moves away from the reference solution and produces much higher temperatures and much structures with stronger emission.

中文翻译：

---

日冕 3D MHD 模拟中热通量演化的非傅立叶描述

摘要 日冕中的热环结构可以通过三维磁流体动力学模拟很好地建模，其中日冕由光球驱动的场线编织加热。为了能够再现与观测相当的发射，必须使用实际的 Spitzer 热导率值，这对这些模拟的时间步长施加了很大的限制，因此计算成本很高。在这里，我们提出了热通量演变的非傅立叶描述，这使我们能够显着加快模拟速度。与半相对论 Boris 校正一起，我们能够限制 Alfvén 速度的时间步长约束并进一步加快模拟速度。我们讨论了这两种方法在 Pencil Code 中的实现，并展示了它们对时间步长、温度结构、欧姆加热速率和日冕模拟中的发射的影响。使用热通量演化的非傅立叶描述以及 Boris 校正，我们可以显着增加模拟的时间步长，而不会远离参考解。但是，对于 3000 及以下的 Alfvén 速度限制值，模拟远离参考解决方案并产生更高的温度和更多具有更强发射的结构。我们可以在不远离参考解决方案的情况下显着增加模拟的时间步长。但是，对于 3000 及以下的 Alfvén 速度限制值，模拟远离参考解决方案并产生更高的温度和更多具有更强发射的结构。我们可以在不远离参考解决方案的情况下显着增加模拟的时间步长。但是，对于 3000 及以下的 Alfvén 速度限制值，模拟远离参考解决方案并产生更高的温度和更多具有更强发射的结构。