WIAS Preprint No. 880, (2003)

Kinetic schemes of selected initial and boundary value problems



Authors

  • Dreyer, Wolfgang
  • Herrmann, Michael
  • Kunik, Matthias
  • Qamar, Shamsul

2010 Mathematics Subject Classification

  • 76Y05 82C40 82C70

Keywords

  • Maximum Entropy Principle, Extended Thermodynamics, kinetic schemes, relativistic Euler equations, conservation laws, hyperbolic systems, shock waves, kinetic theory of phonons

Abstract

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.

Appeared in

  • Analysis and Numerics for Conversation Laws, G. Warnecke, ed., Springer, Berlin [u.a.], 2005, pp. 293-306.

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