Dynamic correction to moment approximations

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 57, Issue 2, 1998, Pages 1668-1672

  Karlin, Iliya V ^a   Gorban, Alexander N ^a   Dukek, G ^b   Nonnenmacher, T F ^b  

^a DORODNICYN COMPUTING CENTER   (Russian Federation)

^b UNIVERSITY OF ULM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001255530     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.57.1668     Document Type: Article

References (20)

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13. Dependence of projectors on the distribution functions was discussed extensively in the paper
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15. Except for Maxwellian molecules (interaction potential U∼r-4) for which L̂φ0≠0 but P2[FL̂φG]=FL̂φ0. Same goes for the relaxation time approximation of the collision integral (L̂=-τ-1).
16. R. F. Rodríguez, Phys. Lett. 107A, 17 (1985); PYLAAG
17. R. E. Nettleton, J. Math. Phys. 36, 1825 (1995); JMAPAQ
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20. In a recent paper, A. N. Gorban and I. V. Karlin, Phys. Rev. E 54, R3109 (1996), alternative Grad-like approximations were suggested, and which use the “moments” of collision integral instead of the moments of the distribution function. When this approximation is taken as the input for the corrections procedure instead of the Grad’s as above, the local corrections satisfy the following integral equations: L̂Yn=bnYn+1, and L̂Zn=anZn+1. Thus, both the inputs have the same limiting eigenvalue problems but proceed to this limit via apparently different sequences of approximations. PLEEE8