Numerical calculation of the self-diffusion, the shear viscosity, and the heat conductivity coefficient for a dilute hard sphere gas

The successive uncorrelated binary collision (SUBC) model is used to calculate numerically the self-diffusion coefficient, the shear viscosity, and the heat conductivity coefficient. It turns out that all three quantities can be represented as infinite sums over all possible successive uncorrelated binary collision sequences weighted by their probability of occurence. Depending on the accuracy required, a certain number of the elements of the infinite sums have to be evaluated. While the Chapman–Enskog procedure gives fast convergence and is therefore useful for numerical calculation, one looses insight in the physical meaning of the approximations. The SUBC model gives a clear picture of what is statistically going on in the sense of the underlying Markoffian nature of the SUBC model. It is briefly shown that the SUBC model and the infinite Chapman–Enskog approximation treats essentially the same problem, namely the solution of the linearized Boltzmann equation. The results obtained can be used not only to describe the dilute limit but also the moderately dense limit, since the higher density contributions, the cross term between the kinetic and the potential terms in the transport ccoefficients, can be expressed by the kinetic terms and δ(t) contributions in the approximate time correlation functions within the SUBC model.