Monte Carlo methods are a powerful tool for the numerical solution of the Boltzmann equation of rarefied
gas dynamics. Their computational complexity is much lower that the one of deterministic methods,
and they are able to handle situations very far from local thermodynamical equilibrium.
When the system is locally close to thermodynamical equilibrium, however, standard Monte Carlo
methods become very inefficient because the collisions are simulated at the rate of the mean
collision time, while macroscopic qualtities change at a much slower rate. A recent approach,
called time relaxer Monte Carlo (TRMC), based on a suitable representation of the solution of
the Boltzmann equation, allows to effectively treat situations in which the system can be close
to local thermodynamical equilibtium, without resolving the small time scale. Some applications
in one and two space dimension will illustrate the effectiveness of the approach.
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