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  • 1
    Electronic Resource
    Electronic Resource
    The Limiting Kinetic Equation of the Consistent Boltzmann Algorithm for Dense Gases (2000)
    Springer
    Journal of statistical physics 101 (2000), S. 1065-1086 
    Details
    ISSN: 1572-9613
    Keywords: kinetic theory ; Enskog equation ; direct simulation Monte Carlo ; Boltzmann equation ; consistent Boltzmann Algorithm ; dense gases
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract This paper establishes a theoretical foundation for the Consistent Boltzmann Algorithm (CBA) by deriving the limiting kinetic equation. The formulation is similar to the proof by one of the authors that the Boltzmann equation is the limiting kinetic equation for Direct Simulation Monte Carlo [W. Wagner, J. Statist. Phys. 66:1011 (1992)]. For a simplified model distilled from CBA, the limiting equation is solved numerically, and very good agreement with the predictions of the theory is found.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1026429722169
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  • 2
    Electronic Resource
    Electronic Resource
    A convergence proof for Bird's direct simulation Monte Carlo method for the Boltzmann equation (1992)
    Springer
    Journal of statistical physics 66 (1992), S. 1011-1044 
    Details
    ISSN: 1572-9613
    Keywords: Boltzmann equation ; Bird's direct simulation Monte Carlo method ; stochastic numerical algorithm ; convergence of random measures ; Markov jump processes
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Bird's direct simulation Monte Carlo method for the Boltzmann equation is considered. The limit (as the number of particles tends to infinity) of the random empirical measures associated with the Bird algorithm is shown to be a deterministic measure-valued function satisfying an equation close (in a certain sense) to the Boltzmann equation. A Markov jump process is introduced, which is related to Bird's collision simulation procedure via a random time transformation. Convergence is established for the Markov process and the random time transformation. These results, together with some general properties concerning the convergence of random measures, make it possible to characterize the limiting behavior of the Bird algorithm.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01055714
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  • 3
    Electronic Resource
    Electronic Resource
    Approximation of the Boltzmann equation by discrete velocity models (1995)
    Springer
    Journal of statistical physics 78 (1995), S. 1555-1570 
    Details
    ISSN: 1572-9613
    Keywords: Boltzmann equation ; discrete velocity models ; weak convergence ; random mass flow
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Two convergence results related to the approximation of the Boltzmann equation by discrete velocity models are presented. First we construct a sequence of deterministic discrete velocity models and prove convergence (as the number of discrete velocities tends to infinity) of their solutions to the solution of a spatially homogeneous Boltzmann equation. Second we introduce a sequence of Markov jump processes (interpreted as random discrete velocity models) and prove convergence (as the intensity of jumps tends to infinity) of these processes to the solution of a deterministic discrete velocity model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02180142
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  • 4
    Electronic Resource
    Electronic Resource
    A random discrete velocity model and approximation of the Boltzmann equation (1993)
    Springer
    Journal of statistical physics 70 (1993), S. 773-792 
    Details
    ISSN: 1572-9613
    Keywords: Discrete velocity models ; Boltzmann equation ; simulation methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract An approximation procedure for the Boltzmann equation based on random choices of collision pairs from a fixed velocity set and on discrete velocity models is designed. In a suitable limit, the procedure is shown to converge to the time-discretized and spatially homogeneous Boltzmann equation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01053594
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