A constructive approach to steady nonlinear kinetic equations

Journal of Computational and Applied Mathematics

Volumn 89, Issue 2, 1998, Pages 199-211

  Babovsky, Hans ^a  

^a ILMENAU UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Kinetic boundary layer; Numerical scheme; Steady kinetic equation

Indexed keywords

BOUNDARY LAYERS; BOUNDARY VALUE PROBLEMS; COMPUTATIONAL METHODS; COMPUTER SIMULATION; KINETIC THEORY; MATHEMATICAL MODELS; NONLINEAR EQUATIONS;

KINETIC BOUNDARY LAYERS; KNUDSEN NUMBER; STEADY NONLINEAR KINETIC EQUATIONS;

EQUATIONS OF MOTION;

EID: 0041171721     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(97)00226-4     Document Type: Article

References (15)

1. K. Aoki, K. Nishino, Y. Sone, H. Sugimoto, Numerical analysis of steady flows of a gas condensing on or evaporating from its plane condensed phase on the basis of kinetic theory: effect of gas motion along the condensed phase, Phys. Fluids A 3 (1991) 2260-2275.
2. L. Arkeryd, C. Cercignani, R. Illner, Measure solutions of the steady Boltzmann equation in a slab, Commun. Math. Phys. 142 (1991) 285-296.
3. H. Babovsky, A convergence proof for Nanbu's Boltzmann simulation scheme, Eur. J. Mech. B/Fluids 8 (1989) 41-55.
4. H. Babovsky, Time averages of simulation schemes as approximations to stationary kinetic equations, Eur. J. Mech. B/Fluids 11 (1992) 199-212.
5. H. Babovsky, Discretization and numerical schemes for stationary kinetic model equations, WIAS preprint No. 179, Berlin, 1995, Comput. Math. Appl., to appear.
6. H. Babovsky, F. Gropengießer, H. Neunzert, J. Struckmeier, B. Wiesen, Application of well-distributed sequences to the numerical simulation of the Boltzmann equation, J. Comput. Appl. Math. 31 (1990) 15-22.
7. H. Babovsky, R. Illner, A convergence proof for Nanbu's simulation method for the full Boltzmann equation, SIAM J. Numer. Anal. 26 (1989) 45-64.
8. H. Babovsky, M. Padula, A new contribution to nonlinear stability of a discrete velocity model, Commun. Math. Phys. 144 (1992) 87-106.
9. C. Cercignani, Mathematical models in rarefied gas dynamics, Surv. Math. Ind. 1 (1991) 119-143.
10. R. Illner, T. Płatkowski, Discrete velocity models of the Boltzmann equation: a survey on the mathematical aspects of the theory, SIAM Rev. 30 (1998) 213-255.
11. R. Illner, J. Struckmeier, Boundary value problems for the steady Boltzmann equation, preprint DMS-708-IR, University of Victoria, Victoria/Canada, 1995.
12. A. Lang, H. Babovsky, W. Cassing, U. Mosel, H.-G. Reusch, K. Weber, A new treatment of Boltzmann-like collision integrals in nuclear kinetic equations, J. Comput. Phys. 106 (1993) 391-396.
13. S.E. Laux, M.V. Fischetti, D.J. Frank, Monte Carlo analysis of semiconductor devices: the DAMOCLES program, IBM J. Res. Develop. 34 (1990) 466-494.
14. H. Neunzert, J. Struckmeier, Particle methods for the Boltzmann equation, Acta Numer. (1995) 417-457.
15. W. Wagner, A convergence proof for Bird's direct simulation Monte Carlo method for the Boltzmann equation, J. Statist. Phys. 66 (1992) 1011-1044.