TWO-DIMENSIONAL MHD NUMERICAL MODEL:

Used model (e.g., Jelinek et al. (2012) where the plasma dynamics is described by a full set of ideal time-dependent MHD equations:

These magnetohydrodynamic equations were transformed into a flux-conserving form (Chung 2002) and solved numerically. We used two types of numerical codes. The first one is based on a modified two-step Lax–Wendroff algorithm (Kliem et al. 2000). In this code the simulation box was covered by a uniform grid with optional number of cells, cell size in both the X and Y directions, the numerical time step and waveguide halfwidth.

Initial conditions can be selected e.g., according to solar flare conditions and perturbations that generate sausage magnetoacoustic waves. The dense slab is embedded in a magnetic environment with a magnetic field given by the plasma beta parameter (optional). The dense slab is considered in equilibrium; therefore, for constant magnetic field the kinetic pressure is also constant everywhere. This also means that the temperature profile across the slab is inverse to the profile of the density.

The mass density profile is considered to be constant along the X axis and is expressed along the Y axis by the formula (Nakariakov & Roberts 1995):

where power index α determines the steepness of the profile, YP is the dense slab center in the Y direction, and w is the half-width of the dense slab.