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The Code

We have developed a code solving CGL-MHD equations (Eqs. 1) using higher-order Godunov methods godunov59. Following [Hirsch (1990)], the scheme involves three distinct steps to obtain the solution at time $t + \Delta t$ from the known solution at time $t$: 1) reconstruction of the left and right states for the solution of generalized Riemann problem, 2) approximation of the fluxes using the Riemann problem solver, 3) advance in time of the average states using the calculated fluxes. To interpolate left and right states we use higher-order-accurate essentially nonoscillatory (ENO) reconstruction [, see][, e.g.]liu98. The calculation of the fluxes is performend with the help of Harten-Lax-val Leer (HLL) approximate Riemann solver harten83. Finally, the time integration is calculated using Runge-Kutta (RK) methods.