Unstructured Orthogonal Meshes for Modeling Coastal and Ocean Flows

Abstract

In this thesis a z?layer unstructured C-grid finite volume hydrostatic model is presented. An efficient and highly scalable implicit technique for the solution of the free surface equation is combined with an Eulerian approach for the advection of momentum. A consistent velocity reconstruc- tion procedure which not only satisfies the continuity law but also guarantees the discrete kinetic energy conservation is presented. It is shown that an ac- curate velocity reconstruction procedure is of crucial importance not only for discretization of the Coriolis term, but also for the correct advection of mo- mentum, especially in the multilayer case. Unlike other z?layer models the method presented here ensures that the staircase representation of bathymetry and free surface has no influence on the vertical structure of the flow. The method is therefore guaranteed to be strictly momentum conservative, also in the layers containing the free surface and bed. A number of test cases are presented to show that the model is able to accu- rately simulate Coriolis dominated flows and flooding and drying processes both in the depth-averaged case and in the presence of multiple z?layers. A simulation of the 2004 Indian Ocean tsunami is used to evaluate the ability of the method to simulate fast propagating tsunami waves and detailed inundation processes. Results obtained using two different rupture models are compared to the tide gauge arrival times, satellite altimetry data and the inundation ob- servations in the Banda Aceh area. The comparison is used not only to assess the quality of the underlying rupture models but also to determine the value of the available data sources for such an assessment. Preliminary results of the unstructured grid fine resolution tidal model the southern North Sea including the Rhine-Scheldt Delta region are presented. The model is able to correctly reproduce the essential characteristics of the M2 tide, as well as of the most important nonlinear shallow water overtides M4 or M6. The simulated velocity field was used to evaluate the Simpson- Hunter stratification parameter, the variability of frontal positions due to tidal advection and spring-neap adjustment.