An ES-BGK model for diatomic gases with correct relaxation rates for internal energies

Navier–Stokes Equations and Bulk Viscosity for a Polyatomic Gas with Temperature-Dependent Specific Heats

“…Figure 1 shows the comparison between the fitting formula (27) with the values in Table 1 and the data in [59,60]. It is seen that the formula (27) reproduces the data well for the temperature range between 220 K and 1100 K. If T − = 300 K and M − = 5, then T + = 1.938T − ≈ 581 K for SF 6 , T + = 3.408T − ≈ 1022 K for CH 4 , and a Read as 7.670 × 10 −2 ; b Value in [31]. 27) with the data in Table 1, the red circles represent the data from [60], and the blue circles denote those from [59].…”

“…In [41], T − and p − are set to be T − = 295 K and p − = 69 mmHg, respectively, in accordance with [31,53], and this T − gives c v (T − )/R = 3.456, γ − = 1.289, and δ − = 3.913. In addition, although the fitting formula (27) with the data in Table 1 is used for c v (T)/R, the exponent s in ( 28) and (29) and Pr are set as s = 0.935 and Pr = 0.73, respectively.…”

“…However, even the simplified versions of the Boltzmann equation are still not simple enough for practical applications. Therefore, alternative approaches using model Boltzmann equations [18][19][20][21][22][23][24][25][26][27] or macroscopic equations [28][29][30][31][32][33][34][35] have been proposed. The model Boltzmann equations bear much simpler structures while retaining certain basic properties of the original Boltzmann equation.…”

Modeling of Ionized Gas Flows with a Velocity-space Hybrid Boltzmann Solver

“…Such relaxation terms include the Bhatnagar-Gross-Krook (BGK) model [10] and its extensions, the ellipsoidal-statistical BGK model (ES-BGK) [11] and the Shakhov model (S-model) [12]. However, the correct incorporation of complex collisional physical phenomena, such as chemical reactions, transitions of internal energy, and complicated scattering laws within the framework of these model equations is still an open question and a topic of active research [13,14,15]. Despite these drawbacks of the linear models, they offer advantages in terms of being scalable to dense regimes [16,17].…”

“…Such relaxation terms include the Bhatnagar-Gross-Krook (BGK) model [10] and its extensions, the ellipsoidal-statistical BGK model (ES-BGK) [11] and the Shakhov model (S-model) [12]. However, the correct incorporation of complex collisional physical phenomena, such as chemical reactions, transitions of internal energy, and complicated scattering laws within the framework of these model equations is still an open question and a topic of active research [13,14,15]. Despite these drawbacks of the linear models, they offer advantages in terms of being scalable to dense regimes [16,17].Another subfamily of the discrete velocity methods does not resort to substituting the collision operator with a simplified model relaxation term, and instead models the full collision process, utilizing remapping procedures to re-distribute post-collisional mass onto the discrete velocity grid [18,19].…”