Stability Analysis and NumericalSimulation of Non-Newtonian Fluidsof Oldroyd KindDen Naturwissenschaftlichen Fakult atender Friedrich-Alexander-Universit at Erlangen-Nurn bergzurErlangung des Doktorgradesvorgelegt vonNicoleta Dana Scurtuaus BrasovAls Dissertation genehmigt von den Naturwissen-schaftlichen Fakult aten der Universit at Erlangen-Nurn bergTag der mundlic hen Prufung: 24. Oktober 2005Vorsitzender derPromotionskommision: Prof. Dr. D.-P. H aderErstberichterstatter: Prof. Dr. Eberhard B anschZweitberichterstatter: Prof. Dr. Wolfgang BorchersTo the man who pleases him,God gives wisdom, knowledge and happiness...(the Bible)AcknowledgmentFirst of all, I am especially thankful to Prof. Dr. Eberhard B ansch who gave me the oppor-tunity to work in his research group in the fascinating eld of computational uid dynamicsand for the time he spent to supervise my research.I also want to thank Prof. Dr. Kunibert G. Siebert who kindly placed his program packageAlbert at my disposal which was the starting point and the major tool for my numericalcomputations.Finally, I want to acknowledge my colleagues from Weierstra Institute Berlin and fromBrandenburg Technical University of Technology Cottbus for their moral encouragement,for text improvements and for their hints concerning computational issues.Erlangen , July 2005 Nicoleta D. ScurtuContentsIntroduction 11 Description of Newtonian and non-Newtonian uids 51.