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Kinetic Schemes for Selected Initial and Boundary Value Problems

In: Analysis and Numerics for Conservation Laws

Author

Listed:
  • Wolfgang Dreyer

    (Weierstrass Institute for Applied Analysis and Stochastics)

  • Michael Herrmann

    (Weierstrass Institute for Applied Analysis and Stochastics)

  • Matthias Kunik

    (Otto-von-Guericke University Magdeburg, Institute for Analysis and Numerics, Faculty of Mathematics)

  • Shamsul Qamar

    (Weierstrass Institute for Applied Analysis and Stochastics
    Otto-von-Guericke University Magdeburg, Institute for Analysis and Numerics, Faculty of Mathematics)

Abstract

Summary The hyperbolic system that describes heat conduction at low temperatures and the relativistic Euler equations belong to a class of hyperbolic conservation laws that result from an underlying kinetic equation. The focus of this study is the establishment of an kinetic approach in order to solve initial and boundary value problems for the two examples. The ingredients of the kinetic approach are: (i) Representation of macroscopic fields by moment integrals of the kinetic phase density. (ii) Decomposition of the evolution into periods of free flight, which are interrupted by update times. (iii) At the update times the data are refreshed by the Maximum Entropy Principle.

Suggested Citation

  • Wolfgang Dreyer & Michael Herrmann & Matthias Kunik & Shamsul Qamar, 2005. "Kinetic Schemes for Selected Initial and Boundary Value Problems," Springer Books, in: Gerald Warnecke (ed.), Analysis and Numerics for Conservation Laws, pages 203-232, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-27907-5_9
    DOI: 10.1007/3-540-27907-5_9
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