The Moment Guided Monte Carlo Method

Abstract

In this work we propose a new approach for the numerical\nsimulation of kinetic equations through Monte Carlo schemes. We\nintroduce a new technique which permits to reduce the variance of\nparticles methods through a matching with a set of suitable\nmacroscopic hydrodynamics equations. In order to preserve correct solutions for all regimes even with the macroscopic model, a non equilibrium term, which couple micro and macro models, is added to the set of fluid equations. The basic idea, on which the method relies, consists in guiding through hydrodynamic equations the particles positions and velocities so that the parallel solution of the fluid and the kinetic models furnishes the same macroscopic quantities.