GPU-accelerated numerical simulations of the Knudsen gas on time-dependent domains

We consider the long-time behaviour of a free-molecular gas in a time-dependent vessel with an absorbing boundary, in any space dimension. We first show, at the theoretical level, that the convergence towards equilibrium heavily depends on the initial data and on the time evolution law of the vessel. Subsequently, we describe a numerical strategy to simulate the problem, based on a particle method implemented on general-purpose graphics processing units (GPGPU). We observe that the parallelisation procedure on GPGPU allows for a marked improvement of the performances when compared with the standard approach on CPU.