Stochastic systems of weighted particles approximating the spatially inhomogeneous Boltzmann equation

ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

Volumn 76, Issue SUPPL. 3, 1996, Pages 215-218

  Rjasanow, S ^a   Wagner, W ^b  

^a University of Koblenz Landau   (Germany)

^b WEIERSTRASS INSTITUTE FOR APPLIED ANALYSIS AND STOCHASTICS   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21444435937     PISSN: 00442267     EISSN: 15214001     Source Type: Journal    
DOI: None     Document Type: Article

References (14)

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2. BIRD, G.: Molecular Gas Dynamics and the Direct Simulation of Gas Flows, Clarendon Press, Oxford, 1994.
3. CERCIGNANI, C., ILLNER, R., PULVIRENTI, M.: The Mathematical Theory of Dilute Gases, Springer, New York, 1994.
4. ILLNER, R., NEUNZERT, H.: On simulation methods for the Boltzmann equation. Transport Theory Statist. Phys. 16 (1987), 141-154.
5. ILLNER, R., RJASANOW, S.: Numerical solution of the Boltzmann equation by random discrete velocity models. European J. Mech. B Fluids 13 (1994), 197-210.
6. ILLNER, R., WAGNER, W.: A random discrete velocity model and approximation of the Boltzmann equation. J. Statist. Phys. 70 (1993), 773-792.
7. NEUNZERT, H., GROPENGIESSER, F., STRUCKMEIER, J.: Computational methods for the Boltzmann equation. In: Applied and Industrial Mathematics (R. Spigler, editor), 111-140. Kluwer Acad. Publ., Dordrecht, 1991.
8. PULVIRENTI, M., ZAVELANI ROSSI, M. B., WAGNER, W.: Convergence of particle schemes for the Boltzmann equation. Eur. J. Mech. B/Fluids 13 (1994), 339-351.
9. RJASANOW, S., WAGNER, W.: A stochastic weighted particle method for the Boltzmann equation, Preprint (Weierstrass Institute for Applied Analysis and Stochastics, Berlin) No. 120 (1994).
10. RJASANOW, S., WAGNER, W.: A generalized collision mechanism for stochastic particle schemes approximating Boltzmann type equations. (in preparation)
11. SCHREINER, M.: Weighted particles in the finite pointset method. Transport Theory Statist. Phys. 22 (1993), 793-817.
12. WAGNER, W.: A convergence proof for Bird's direct simulation Monte Carlo method for the Boltzmann equation. J. Statist. Phys. 66 (1992), 1011-1044.
13. WAGNER, W.: Stochastic systems of particles with weights and approximation of the Boltzmann equation. The Markov process in the spatially homogeneous case. Stochastic Anal. Appl. 12 (1994), 639-659.
14. WAGNER, W.: Approximation of the Boltzmann equation by discrete velocity models. J. Statist. Phys. 78 (1995), 1555-1570.