Nonequilibrium velocity distribution function of gases: Kinetic theory and molecular dynamics

Abstract

In the first part of this paper the moment method is employed to solve the nonlinear Boltzmann equation. An expansion about a local Maxwellian distribution is used with the basis functions introduced by Waldmann [in Handbuch der Physik, edited by S. Flügge (Springer, Berlin, 1958), Vol. 12, p. 295]. Earlier approaches are extended by the inclusion of more expansion functions (Sonine polynomials) in order to obtain an approximation for the velocity distribution function. General relations for the coupling of the moments are derived and the resulting transport relaxation equations are solved for the special Couette geometry. The influence of the higher moments on the viscosity coefficients is small, but the higher moments are essential for the distribution function itself. The inclusion of the quadratic collision matrix elements leads to minor modifications only. In another part of the paper the velocity distribution function is obtained from nonequilibrium molecular dynamics. Excellent agreement with the predictions of the moment method is found provided that the constant temperature constraint of the simulation is taken into account by incorporating a nonconservative external force term into the Boltzmann equation. The effect of this modification is discussed in detail for the viscosity coefficients. The non-Newtonian flow behavior of gases is studied on the microscopic level of the velocity distribution function. In addition an isotropic distortion of the Maxwellian distribution is observed.