DETERMINATION OF THE GENERALIZED POTENTIALS IN THE MODIFIED MOMENT METHOD FOR THE BOLTZMANN-EQUATION

The modified moment method for the Boltzmann equation requires the determination of the unknowns (generalized potentials) in the nonequilibrium canonical distribution function in terms of conserved and nonconserved macroscopic variables in a way consistent with the matching conditions for the conserved variables. In the past, they were determined to the lowest order by a perturbation method and used for studying nonlinear transport processes in gases. In this paper, we determine them to a higher order and then resum them to forms applicable to a wider range of validity. As a mathematically more appropriate alternative to the resummation method, a set of Volterra-type integral equations is also derived for the generalized potentials and their solution is discussed. These linear integral equations provide ways to determine the unknowns (generalized potentials) nonperturbatively and systematically.