2007
DOI: 10.1209/0295-5075/79/60001
|View full text |Cite
|
Sign up to set email alerts
|

Computer-aided kinetic theory and granular gases

Abstract: A novel computer-aided method for solving kinetic equations has been developed and implemented in a study of the Boltzmann equation corresponding to elastic and inelastic hard spheres. Accurate results are obtained for the linear transport coefficients for all physical values of the coefficient of normal restitution, α. These coefficients are bounded and nonsingular even in the limit of vanishing α. Using the new method we also calculated the full homogeneous cooling state (HCS) distribution function (after re… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
1
1

Citation Types

6
50
0

Year Published

2009
2009
2024
2024

Publication Types

Select...
3
3

Relationship

0
6

Authors

Journals

citations
Cited by 42 publications
(56 citation statements)
references
References 19 publications
6
50
0
Order By: Relevance
“…The difference between the results from the two simulations could be due to velocity correlations in the correlation function present in the GK relation for the shear viscosity (Garzó et al 2007). In comparison to the results from the modified version of the first Sonine approximation (dash-dotted magenta line), the present results for the reduced shear viscosity (solid black line) are in better agreement with the DSMC simulations of Garzó et al (2007) in the elastic (e = 1) case, the theoretical expressions of Noskowicz et al (2007) lead to η * = 1.01205 while the DSMC simulations of Garzó et al (2007) give η * ≈ 1.016. Thus, in the elastic (e = 1) case, η * ≈ 1.014851 from the expression (5.23) 1 obtained here is much closer to its true value in comparison to that from the theoretical expressions of Noskowicz et al (2007).…”
Section: Comparison With Existing Theories and Computer Simulationssupporting
confidence: 72%
See 2 more Smart Citations
“…The difference between the results from the two simulations could be due to velocity correlations in the correlation function present in the GK relation for the shear viscosity (Garzó et al 2007). In comparison to the results from the modified version of the first Sonine approximation (dash-dotted magenta line), the present results for the reduced shear viscosity (solid black line) are in better agreement with the DSMC simulations of Garzó et al (2007) in the elastic (e = 1) case, the theoretical expressions of Noskowicz et al (2007) lead to η * = 1.01205 while the DSMC simulations of Garzó et al (2007) give η * ≈ 1.016. Thus, in the elastic (e = 1) case, η * ≈ 1.014851 from the expression (5.23) 1 obtained here is much closer to its true value in comparison to that from the theoretical expressions of Noskowicz et al (2007).…”
Section: Comparison With Existing Theories and Computer Simulationssupporting
confidence: 72%
“…The dash-dotted (magenta) lines display the results obtained with the theoretical expressions for the reduced transport coefficients deduced through the modified version of the first Sonine approximation in Garzó et al (2007). The squares are the results obtained with the theoretical expressions derived via the so-called computer-aided method devised by Noskowicz et al (2007) while the triangles denote the numerical solution of the Boltzmann equation obtained through Green-Kubo (GK) relations by means of the direct-simulation Monte Carlo (DSMC) method (Bird 1994) in Brey et al (2005). The circles in figure 5 also denote the DSMC simulation results from Montanero et al (2005) obtained with another method-by the implementation of an external force which compensates for the collisional cooling.…”
Section: Comparison With Existing Theories and Computer Simulationsmentioning
confidence: 99%
See 1 more Smart Citation
“…Using the asymptotic high-velocity tail (10), Noskowicz et al [8] have shown that a k ∝ (−4/ξ 2 ) k (k + 1)! for large k, so that the series (11) (15) with (λ 0 , λ 1 , λ 2 ) = (104.1, −51.43, 78.67), confirmed that vNE's expression overestimates a 2 for α 0.5, while the alternative expression proposed in Ref.…”
Section: A Brief Review Of Previous Resultsmentioning
confidence: 99%
“…On the other hand, It is known that in the high-inelasticity region α 0.6 (i.e., once a 2 becomes positive) the higherorder Sonine coefficients are no longer negligible [8,14,17], so that the linear approximations based on the neglect of nonlinear terms and of a k with k ≥ 3 or k ≥ 4 are not a priori reliable. This is made evident by the lack of selfconsistency of different linear approximations used to estimate a 2 from the first non-trivial equation of the moment hierarchy, as shown in Fig.…”
Section: Discussionmentioning
confidence: 99%