An implicit Monte arlo method for rarefied gas dynamics - 1. The space homogeneous case

For the space homogeneous Boltzmann equation, we formulate a hybrid Monte C arlo method that is robust in the fluid dynamic limit. This method is based on an analytic representation of the solution over a single time step and involves implicit time differencing derived from a suitable power series ex pansion of the solution (a generalized Wild expansion), A class of implicit , yet explicitly implementable, numerical schemes is obtained by substituti ng a Maxwellian distribution in place of the high order terms in the expans ion. The numerical solution is represented as a convex combination of a non -equilibrium particle distribution and a Maxwellian. The hybrid distributio n is then evolved by Monte Carlo using the implicit formulation for the tim e evolution. Computational simulations of spatially homogeneous problems by our method are presented here for the Kac model and for the variable hard sphere model (including Maxwell molecules). Comparison to exact solutions a nd to direct simulation Monte Carlo (DSMC) computations shows die robustnes s and the efficiency of the new method, (C) 1999 Academic Press.