Threaded-Field-Line Model for the Transition Region and Solar Corona

In numerical simulations of the solar corona, both for the ambient state and especially for dynamical processes the most computational resources are spent for maintaining the numerical solution in the Low Solar Corona and in the transition region, where the temperature gradients are very sharp and the magnetic field has a complicated topology. The degraded computational efficiency is caused by the need in a highest resolution as well as the use of the fully three-dimensional implicit solver for electron heat conduction. On the other hand, the physical nature of the processes involved is rather simple (which still does not facilitate the numerical methods) as long as the heat fluxes as well as slow plasma motional velocities are aligned with the magnetic field. The Alfven wave turbulence, which is often believed to be the main driver of the solar wind and the main source of the coronal heating, is characterized by the Poynting flux of the waves, which is also aligned with the magnetic field. Therefore, the plasma state in any point of the three-dimensional grid in the Low Solar Corona can be found by solving a set of one-dimensional equations for the magnetic field line ("thread"), which passes through this point and connects it to the chromosphere and to the global Solar Corona. In the present paper we describe an innovative computational technology based upon the use of the magnetic-field-line-threads to forlmulate the boundary condition for the global solar corona model which traces the connection of each boundary point to the cromosphere along the threads.