In the present work, we present a novel numerical algorithm to couple the Direct Simulation Monte Carlo method (DSMC) for the solution of the Boltzmann equation with a finite volume like method for the solution of the Euler equations.
Recently we presented in ,, different methodologies which permit to solve fluid dynamics problems with localized regions of departure from thermodynamical equilibrium. The methods rely on the introduction of buffer zones which realize a smooth transition between the kinetic and the fluid regions.
In this talk we extend the idea of buffer zones and dynamic coupling to the case of the Monte Carlo methods. To facilitate the coupling and avoid the onset of spurious oscillations in the fluid regions which are consequence of the coupling with a stochastic numerical scheme, we use a new technique which permits to reduce the variance of the particle methods . In addition, the use of this method permits to obtain estimations of the breakdowns of the fluid models less affected by fluctuations and consequently to reduce the kinetic regions and optimize the coupling.
 P.Degond, S.Jin, L. Mieussens, A Smooth Transition Between Kinetic and Hydrodynamic Equations , Journal of Computational Physics, Vol. 209, pp. 665-694, (2005).
 P.Degond, G. Dimarco, L. Mieussens., A Moving Interface Method for Dynamic Kinetic-fluid Coupling. J. Comp. Phys., Vol. 227, pp. 1176-1208, (2007).
 P.Degond, G. Dimarco, L. Mieussens., A Multiscale Kinetic-Fluid Solver with Dynamic Localization of Kinetic Effects. J. Comp. Phys., Vol. 229, pp.4907-4933, (2010).
 P. Degond, G. Dimarco, L. Pareschi, The Moment Guided Monte Carlo Method, To appear in International Journal for Numerical Methods in Fluids.