A Monte Carlo method for the Broadwell model with relaxation

A Monte Carlo method is proposed for numerical solution of the Broadwell model. Developing a probabilistic interpretation of the equations, the transport and collision parts are treated separately in the method. Particles are advected according to their velocities and collisions are performed between randomly chosen particles. We numerically test the algorithm for a variety of examples. In particular we are interested in situations which generate structures that have nonsmooth fronts. Our simulations show that this Monte Carlo method is capable of capturing the nonlinear regime in presence of shocks and interactions. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)