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Continuum Mechanics and Thermodynamics

, Volume 12, Issue 6, pp 403–421 | Cite as

The cumulant method for computational kinetic theory

  • Steffen Seeger
  • Heinz Hoffmann
Original Articles

We propose a new method for numerical simulation of gas dynamics based on kinetic theory. The method is based on a cumulant-expansion-ansatz for the phase space density, which leads to a set of quasi-linear, hyperbolic partial differential equations. The method is compared to the moment method of Grad. Both methods agree for low-order approximations but the method proposed shows additional non-linear terms for high order approximations. Boundary conditions on the cumulants for an ideally reflecting and an ideally rough boundary surface are derived from conditions on the phase space density. A Lax-method is used for numerical analysis of a 2d-BGK fluid, which results in an easy-to-implement algorithm well suited for implementation on massivly parallel computers. The results are found to agree qualitatively with predictions from moment theories.

Keywords

Boundary Condition Differential Equation Phase Space Partial Differential Equation Kinetic Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Steffen Seeger
    • 1
  • Heinz Hoffmann
    • 1
  1. 1.Institut für Physik, Technische Universität Chemnitz, 09107 Chemnitz, Germany DE

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