Numerical methods for multiphase mixture conservation laws with phase transition [Elektronische Ressource] / von Ali Zein

Numerical methods for multiphase mixtureconservation laws with phase transitionDissertationzur Erlangung des akademischen Gradesdoctor rerum naturalium(Dr. rer. nat.)von Ali Zein, M.Sc.geb. am 12. Februar 1978 in Hebron, Pal¨astinagenehmigt durch die Fakult¨at fu¨r Mathematikder Otto-von-Guericke-Universit¨at MagdeburgGutachter:Prof. Dr. Gerald WarneckeProf. Dr. Philippe HelluyEingereicht am: 7. April 2010Verteidigung am: 28. Juni 2010AbstractTheseven-equationmodelforcompressibletwo-phaseflowsisafullnon-equilibriummodel;each phase has its own pressure, velocity, temperature, etc. A single value for each prop-erty, an equilibrium value, can be achieved by relaxation methods. This model has betterfeatures than other reduced models of equilibrium pressure for the numerical approxi-mations in the presence of non-conservative terms. In this thesis, we modify this modelto include the heat and mass transfer. We insert the heat and mass transfer throughtemperature and Gibbs free energy relaxation effects. New relaxation terms are modeledand new numerical procedures for the instantaneous temperature and Gibbs free energyrelaxation toward equilibrium are proposed.