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On simulation methods for solving the Boltamann equation

Über Simulationsmethoden zur Lösung der Boltzmanngleichung

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Abstract

We will give an overview of the problem and then show how to modify an already present algorithm, so that it is also useful from a practical point of view. Further we will show that this algorithm is suitable for parallel computing and prove by means of an example that it can compete with the Bird algorithm, which is almost always applied by engineers but has only a heuristic base.

Zusammenfassung

Wir geben einen Überblick über die Problemstellung und zeigen dann, wie man einen bereits vorhandenen Algorithmus modifizieren kann, so daß er auch praktisch verwendbar wird. Wir zeigen weiter, daß dieser Algorithmus für Parallelrechner geeignet ist und weisen anhand eines Beispiels seine Konkurrenzfähigkeit gegenüber dem von den Ingenieuren fast ausschließlich verwendeten Bird-Algorithmus nach.

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References

  1. Cercignani, C.: Theory and Application of the Boltzmann Equation. New York: Elsevier 1975.

    Google Scholar 

  2. Bird, G. A.: Molecular Gas Dynamics. Oxford: Clarendon Press 1976.

    Google Scholar 

  3. Nanbu, K.: Interrelations between various direct simulation methods for solving the Boltzmann equation. J. Phys. Soc. Japan52, 3382 (1983).

    Google Scholar 

  4. Nanbu, K.: Direct simulation scheme derived from the Boltzmann equation. J. Phys. Soc. Japan49, 2042 (1980a).

    Google Scholar 

  5. Macrossan, M. N.: Diatomic Collision Models Used in the Monte Carlo Direct Simulation Method Applied to Rarefied Hypersonic Flows. Ph. D. Thesis, University of London 1983.

  6. Ploss, H.: Simulationsmethoden zur Lösung der Boltzmanngleichung. Bericht der Arbeitsgruppe Technomathematik Nr. 11, Universität Kaiserslautern 1985.

  7. Babovsky, H.: On a simulation scheme for the Boltzmann equation. Math. Meth. Appl. Sci.9, to appear (1986).

  8. Nanbu, K.: Analysis of cylindrical Couette flows by use of the direct simulation method. Phys. Fluids27, 2632 (1984).

    Google Scholar 

  9. Gentzsch, W.: Vectorization of Computer Programs with Applications to Computational Fluid Dynamics. Braunschweig; Wiesbaden: Vieweg 1984.

    Google Scholar 

  10. Nanbu, K., Watanabe Y.: Analysis of the Internal Structure of Shock Waves by Means of the Exact Direct-Simulation Method. Rarefield Gas Dynamics, 14th Symposium, p. 183. University of Tokyo Press 1984.

  11. Alsemeyer, H.: Density profiles in Argon and nitrogen shock waves measured by the absorption of an electron beam. J. Fluid Mech.74, 497 (1976).

    Google Scholar 

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Ploss, H. On simulation methods for solving the Boltamann equation. Computing 38, 101–115 (1987). https://doi.org/10.1007/BF02240176

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  • DOI: https://doi.org/10.1007/BF02240176

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