Moment conserving method for modelling multiple collisions in particle simulations

A statistical procedure for modelling the cumulative effect of multiple collisions in particle simulations is presented. The procedure approximates the probability density function (PDF) of the final scattering angle and that of the particle net displacement by parametric functions. Formulae for determining the moments of the exact PDFs as a function of the statistics of a single collision event are derived. Using these formulae, the parametric functions can be fitted to yield the same first moments as the real distributions. Therefore, in contrast to other approaches where after one iteration the error in the first moments depends on the number of collisions modelled, the present model provides always the right moments. Correlation between the scattering angle and the displacement of the particle is also considered and enforced by means of a Gaussian copula.