Multidimensional schemes for hyperbolic conservation laws on triangular meshes [Elektronische Ressource] / von Qurrat-ul-Ain

Multidimensional Schemesfor Hyperbolic Conservation Lawson Triangular MeshesQurrat-ul-AinFakultat fur Mathematik¨ ¨Otto-von-Guericke Universitat Magdeburg¨Multidimensional Schemes for HyperbolicConservation Laws on Triangular MeshesDissertationzur Erlangung des akademischen Gradesdoctor rerum naturalium(Dr. rer. nat.)genehmigt durch die Fakultat fur Mathematik¨ ¨der Otto-von-Guericke-Universita¨t Magdeburgvon M.Phil Physik Qurrat-ul-Aingeb. am 02. Januar 1970 in Mardan, PakistanGutachter:Prof. Dr. Jiequan LiProf. Dr. M´aria Luk´aˇcov´aProf. Dr. Gerald WarneckeEingericht am: 1. Marz 2005¨Verteidigung am: 25. April 2005AbstractIn this dissertation we present two kinds of multidimensional schemes for hyperbolic sys-temsbasedon triangularmeshes. Thefirstkind ofschemesareevolutionGalerkinschemes(EG) which are truly multidimensional schemes and the second kind is a new space-timeconservative central-type method which we name a slope propagation (SP) method.Our first scheme is an extension of the EG schemes for hyperbolic systems from rectan-gular to triangular meshes. We develop EG schemes for the linear wave equation system,the nonlinear wave equation system, the linearized Euler equations, the advection waveequation system and the nonlinear Euler equations for structured/unstructured triangularmeshes. We have also extended these EG schemes on triangular meshes to second order byusing linear reconstruction.