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 Markovia n evolution of a probability vector, whose moments represent the macro scopic quantities of the gas. Convergence of the probability vector to wards the equilibrium steady state is proven when the walls are at a t emperature compatible with the equilibrium itself. A physical applicat ion is subsequently dealt with. The classical problem of heat transfer between two parallel plates at different temperatures is formulated a nd solved, and the properties of the final steady state are discussed.