Fig. 10

Difference in the spectrum of spontaneous RBS. Results for G13, R13, and R26 moment equations are obtained from Fig. 9a, while others are \(\int _{\infty }^{\infty } |S_{{GH}}^{N}-S_{{GH}}^{N=60}| df_{s}\) with \(S_{{GH}}^{N}\) being the spectrum obtained by solving the Shakhov kinetic model (44) with the Gauss-Hermite quadrature of order N; in three-dimensional molecular velocity space v, the number of total discrete velocity points is N³, while the corresponding Grad moment equations have (N+1)(N+2)(N+3)/6 moments [19]. Note that before the comparison, areas of RBS spectra are normalized to unity. The solution may be viewed to be accurate when the relative difference is less than 0.05. Also note that the relative difference when N=5,7,10 and 20 does not decrease with Kn when Kn≲0.1 is probably because in spontaneous RBS the spectrum between the Rayleigh and Brillouin peaks is nearly zero [see Fig. 2a] so any difference is magnified