Discontinuous Galerkin methods for the unsteady compressible Navier-Stokes equations [Elektronische Ressource] / by Gregor Gassner

Discontinuous Galerkin Methods for the UnsteadyCompressible Navier-Stokes EquationsA thesis accepted by the Facultyof Aerospace Engineering and Geodesy of the Universit¨at Stuttgartin partial fulfilment of the requirements for the degree ofDoctor of Engineering Sciences (Dr.-Ing.)byGregor Gassnerfrom FussachMain-referee : Prof. Dr. Claus-Dieter MunzCo-referee : Prof. Dr. Jan S. HesthavenDate of defence : 19.1.2009Institut fu¨r Aerodynamik und GasdynamikUniversit¨at Stuttgart2009Fu¨r Annemarie, Josef, Veronika, Karolin, Johanna und Emanuel.iiiPrefaceThisthesiswasdeveloped duringmyworkasscientific employee at theInstitutfu¨r Aero- und Gasdynamik of the Universit¨at Stuttgart.Many thanks to my doctoral supervisor Prof. Dr. Claus-Dieter Munz forthe exceptional working conditions in his research group, especially for all thescientific freedom I was granted under his supervision.The work was financed by Deutsche Forschungsgemeinschaft (DFG).Manythanksalsotoallmycolleagues at IAGfor thegood workingatmosphereandallthefruitfulscientificdiscussionstheyhadwithmeinthelastthreeyears.A special thank at this place to my colleague Frieder L¨orcher.Stuttgart, 3. September 2008Gregor GassnerivContentsSymbols viiAbbreviations xKurzfassung xiAbstract xii1 Introduction 11.1 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Discontinuous Galerkin for Compressible Navier-Stokes. . . . . 21.3 Tensor and Differentiation Operator Notations .