THE SEMICONTINUOUS BOLTZMANN EQUATION: TOWARDS A MODEL FOR FLUID DYNAMIC APPLICATIONS

This paper proposes a semicontinuous model of the Boltzmann equation for gas particles moving in the plane in all possible directions, but with a finite, large, number of velocity moduli. The model, called the n-semicontinuous Boltzmann equation, consists in a system of integro-differential equations with one-fold integrals over a suitable angular variable. Thermodynamic equilibrium is studied in details. The model is then applied to the analysis of a temperature jump problem. The results are compared with the ones obtained by continuous models of the Boltzmann equation.