Proposed and developed by Antiochos 2013; Dahlin et al. 2022b, the “Statistical Injection of Condensed Helicity” (STITCH) model accounts for the small-scale effect of the convection (circulation) motions in the chromosphere/transition region/low corona. For a uniform isotropic turbulence, the chaotic small-scale and high frequency velocity would cancel in average. However, with any spatial gradient along the solar surface ('horizontal' gradient), the larger rotational velocity of a stronger nearby vortex is not fully balanced by the opposite rotation of a smaller vortex, thus resulting in the averaged larger-scale motion.

The key point of the revisited STITCH formulation is that we assume that the larger-scale motion occurs along the level lines of constant radial, field, particularly, along the banks of the polarity inversion line two oppositely propagating shear flows producing the magnetic shear and electric current along the PIL.

We provide the results of numerical simulations based on the extit{characteristic} boundary condition for the MHD equations above the low boundary of the computational domain Depending on the plasma motion and magnetic field near the boundary, the boundary condition adjusts the solution to the large-scale motion velocity of the STITCH model. The analysis of thus obtained magnetic configurations will be reported.