Nonlinear evolution of probability vectors of interest in discrete kinetic theory

In the framework of the discrete Boltzmann equation, a suitable space-time discretization of the one-dimensional fourteen discrete velocity model by Cabannes, leads in a bounded domain to the nonlinear Markovian evolution of a probability vector, whose moments represent the macroscopic quantities of the gas. Convergence of the probability vector towards the equilibrium steady state is proven when the walls are at a temperature compatible with the equilibrium itself. A physical application is subsequently dealt with. The classical problem of heat transfer between two parallel plates at different temperatures is formulated and solved, and the properties of the final steady state are discussed.