Solution-adaptive moving mesh solver for geophysical flows [Elektronische Ressource] / Christian Kühnlein. Betreuer: Ulrich Schumann

Solution-adaptive moving meshsolver for geophysical flowsChristian KühnleinMünchen 2011iiSolution-adaptive moving meshsolver for geophysical flowsChristian KühnleinDissertationan der Fakultät für Physikder Ludwig–Maximilians–UniversitätMünchenvorgelegt vonChristian Kühnleinaus NürnbergMünchen, Februar 2011Erstgutachter: Prof. Dr. Ulrich SchumannZweitgutachter: Prof. Dr. George CraigTag der mündlichen Prüfung: 18.04.2011Für meine Familie.viAbstractDynamical processes occurring in geophysical flows are characterised by the nonlin-ear interaction of various scales of motion. The accurate numerical representationof such flows is limited by the available number of mesh points covering the domainof interest. Numerical simulations applying uniformly distributed grid cells wastemesh points in regions of large motion scales whereas coexisting small-scale pro-cesses cannot be adequately resolved.The current thesis offers the design, implementation, and application of an adaptivemoving mesh algorithm for dynamically variable spatial resolution to the numericalsimulation of nonlinear geophysical flows. For this purpose, the established geophys-ical flow solver EULAG was modified and extended. The non-hydrostatic, anelasticequations of EULAG are rigorously implemented in time-dependent generalised co-ordinates. This setting enables moving mesh adaptation by solving the equations ina straightforward approach developed in this thesis.