Numerical Solution of the Nonlinear Boltzmann Equation for Nonequilibrium Gas Flow Problems

Binary scattering model for Lennard-Jones potential: Transport coefficients and collision integrals for non-equilibrium gas flow simulations

“…For l=3, there are no collision integrals tabulated by Hirschfelder et al 10 and hence W 3 (1) was chosen. The agreement between the exact LJ collision integrals and the LJPA model is excellent once again with the maximum error being about 2.8% for W (3) (1) and 3.7% for W (4) (4). For the GSS model, the errors were computed only for 0.3 ≤ kT / LJ ≤ 400 since the error is very high outside this range.…”

“…For W (4) (4), the maximum error using GSS model is about 20% with the error being greater than 8% for kT / LJ ≤ 1.25. On the other hand, for W (3) (1), the maximum error using GSS model is about 22% with the error being greater than 8% for kT / LJ ≤ 90. Other values of n have not been reported here for l = 3 and l = 4 but the error trends were very similar.…”

“…In order to perform detailed comparisons, the variation of the cross sections S (1) , S (2) , S (3) , and S (4) for the LJPA model, exact LJ scattering angle, and the GSS model are compared in Figure 1. The functional forms of S (l) for l = 1, 2, 3, and 4 using Eq.…”

“…1) method or deterministically by a discrete velocity method. [2][3][4][5] Transport in gases is completely determined by molecular properties such as the intermolecular potential and molecular mass which constitute the molecular model required for the solution of the Boltzmann equation. Molecular models with purely repulsive interaction such as the hard sphere 6 or the Maxwell molecules 1 lead to mathematical simplifications that provide certain advantages in solving the Boltzmann equation using discrete velocity methods and hence are widely used.…”

“…where T m is the melting temperature in K, k is the Boltzmann's constant, and V m, sol is the solid state molar volume in cm 3 /mol. For common gases, such as nitrogen and argon, which have relatively shallow potential well ( LJ ≤ 100 K), the attractive component becomes important at low temperature conditions often encountered in, for example, supersonic flow experiments.…”