Technische Universit¨at Mu¨nchenFachgebiet HydromechanikCompact fourth-order scheme for numericalsimulations of Navier-Stokes EquationsARPIRUK HOKPUNNAVollsta¨ndiger Abdruck der von der Fakult¨at fu¨r Bauingenieur- und Vermessungswesen derTechnischen Universitat Munchen zur Erlangung des akademischen Grades eines¨ ¨Doktor-Ingenieursgenehmigten Dissertation.Vorsitzender: Univ.-Prof. Dr.-Ing. Dr.-Ing. habil. Gerhard M. Muller¨Pru¨fer der Dissertation:1. Univ.-Prof. Dr.-Ing. habil. Michael Manhart2. Univ.-Prof. Dr.rer.nat Barbara Wohlmuth, Universitat Stuttgart¨Die Dissertation wurde am 23.09.2009 bei der Technischen Universitat Munchen eingereicht und¨ ¨durch die Fakult¨at fu¨r Bauingenieur- und Vermessungswesen am 10.12.2009 angenommen.AcknowledgementsI would like to thank colleagues at Fachgebiet Hydromechanik of Technische Universit¨atMunchen and express my special appreciation to Prof. M. Manhart for supervising my¨research. His insightful suggestions have always been a guided light for my work. All of mywork would not be made possible with out his constant helps and supports. I would like toexpress my sincere gratitude to Dr.-Ing. M. Haselbauer, Dr.-Ing. F. Schwertfirm, Dipl.-Ing.N. Peller. and Dipl.-Tech. math. C. Gobert. Discussion with them during coffee breakshave always beenenjoyable momentsandmostofthetime, comealongsome newinterestingideas. Many thanks to Dr.-Ing. C.