The Moment Guided Monte Carlo Method

In this work we propose a new approach for the numerical simulation of kinetic equations through Monte Carlo schemes. We introduce a new technique which permits to reduce the variance of particles methods through a matching with a set of suitable macroscopic 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.