  Recently a new class of Monte Carlo methods, called Time Relaxed Monte Carlo
(TRMC), designed for the simulation of the Boltzmann equation close to fluid
regimes have been introduced. A generalized Wild sum expansion of the solution
is at the basis of the simulation schemes. After a splitting of the equation
the time discretization of the collision step is obtained from the Wild sum
expansion of the solution by replacing high order terms in the expansion with
the equilibrium Maxwellian distribution; in this way speed up of the methods
close to fluid regimes is obtained by efficiently thermalizing particles close
to the equilibrium state. In this work we present an improvement of such
methods which allows to obtain an effective uniform accuracy in time without
any restriction on the time step and subsequent increase of the computational
cost. The main ingredient of the new algorithms is recursivity. Several
techniques can be used to truncate the recursive trees generated by the schemes
without deteriorating the accuracy of the numerical solution. Techniques based
on adaptive strategies are presented. Numerical results emphasize the gain of
efficiency of the present simulation schemes with respect to standard DSMC
methods.
