The energy analysis for the monte carlo simulations of a diffusive shock

According to the shock jump conditions, the total fluid's mass, momentum, and energy should be conserved in the entire simulation box. We perform the dynamical Monte Carlo simulations with the multiple scattering law for energy analysis. The various energy functions of time are obtained by monitoring the total particles' mass, momentum, and energy in the simulation box. In conclusion, the energy analysis indicates that the smaller energy losses in the prescribed scattering law are, the harder the energy spectrum produced is.