Convergency of the Monte Carlo algorithms for linear transport modeling Original Research Article

We consider the convergency of the basic Monte Carlo (MC) algorithms for solving the Boltzmann transport equation (BTE). It is a linear kinetic equation describing a broad class of particle transport phenomena such as electron and neutron transport, radiative transfer, medium energy electron and ion scattering in solids, etc. The variety of the MC algorithms can be summarized in three main groups. The algorithms of the first one simulate the natural chain of events, happening during the physical process of the particle transport. The algorithms belonging to the other two generate the particle history back in time or modify the weight of the elementary events, thus achieving variance reduction in desired regions of the phase space. It has been shown that all of them can be generated by the iteration approach (IA) – a method for obtaining MC algorithms by applying numerical MC techniques to the integral form of the BTE. The convergence proof is based on the IA and the convergence of the Neumann series of the integral form of the BTE. A discussion of the probable error is presented.