Kinetic schemes for the relativistic hydrodynamics [Elektronische Ressource] / von Shamsul Qamar

Kinetic Schemes for theRelativistic HydrodynamicsShamsul QamarFakulta¨t fu¨r MathematikOtto-von-Guericke Universita¨t MagdeburgKinetic Schemes for the Relativistic HydrodynamicsDissertationzur Erlangung des akademischen Gradesdoctor rerum naturalium(Dr. rer. nat.)genehmigt durch die Fakult¨at fu¨r Mathematikder Otto-von-Guericke-Universitat Magdeburg¨von M.Phil Math. Shamsul Qamargeb. am 12. Marz 1972 in Mardan, Pakistan¨Gutachter:Prof. Dr. M´aria Luk´aˇcov´aProf. Dr. Thomas SonarProf. Dr. Gerald WarneckeEingereicht am: 5. Mai 2003Verteidigung am: 26. September 2003Betreuer:Dr. Matthias KunikProf. Dr. Gerald WarneckeAbstractKinetic schemes for the relativistic Euler equations are presented, which describe the flow ofa perfect gas in terms of the particle densityn, the spatial part of the four-velocityu and thepressure p. The physical frame in the whole study will be exclusively special relativity. Weconsider both, the ultra-relativisticEuler equations, and a more general form of the relativis-tic Euler equations. The general form of relativistic Euler equations covers the whole rangefrom the non-relativistic to the ultra-relativistic limit. We also consider as a special case thenon-relativistic theory. The basic ingredients of the kinetic schemes are the phase density inequilibrium and the free-flight. The phase density generalizes the non-relativistic Maxwellianfor a gas in local equilibrium.