Kinetic Schemes for Selected Initial and Boundary Value Problems

Wolfgang Dreyer (), Michael Herrmann (), Matthias Kunik () and Shamsul Qamar ()
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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

A chapter in Analysis and Numerics for Conservation Laws, 2005, pp 203-232 from Springer

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.

Keywords: Boltzmann-Peierls equation; hyperbolic moment systems; Bose-gas; phonons; relativistic Euler equations; kinetic schemes; maximum entropy principle; shock waves (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1007/3-540-27907-5_9

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