Application of a generalized total variation diminishing algorithm to cosmic ray transport and acceleration

We have applied a modified total variation diminishing (TVD) method within the framework of a finite difference method for solving a transport equation for cosmic rays in an irregular magnetic field. We employ Roe's superbee scheme to control the numerical diffusion at a sharp profile in the cosmic ray particle density. Furthermore, we have modified the TVD concept for the case of a general Courant number. Comparison with previous results shows that this technique can give an accurate solution with an increased grid size and much shorter running time. This has also enabled the first simulations of the pitch angle transport and acceleration of cosmic rays crossing an oblique shock discontinuity at moderate energies.