On the development of a ghost-cell immersed boundary method and its application to large eddy simulation and geophysical fluid dynamics

Complex geometry is found in a variety of engineering and geophysical applications. The availability of accurate and efficient methods for dealing with arbitrary complex geometry would represent a significant contribution. This thesis develops and validates an efficient ghost-cell immersed boundary method (GCIBM). The GCIBM allows systematic development of numerical schemes for treating the immersed boundary while preserving the accuracy of the base solver. The GCIBM module is implemented in several existing numerical codes. The results are compared with experiments and/or boundary-fitted results. The test cases include two-dimensional flow over a circular cylinder, three-dimensional turbulent flow over a wavy boundary, and stratified flow over a three-dimensional Gaussian bump. The numerical results agree well with published experimental and/or boundary-fitted grid results. We also investigate eddy formation and the effects of coastal geometry on coastal upwelling. Mixing and stirring are quantified using a mixedness parameter and energy budgets. Finally, we extend the GCIBM to simulate the coastal circulation in the vicinity of Monterey Bay and compare the simulation results with observation. The mean currents follow the annual cycle of the seasonal circulation. The coastal geometry plays an important role in the generation and movement of coastal eddies. We also study the effects of Monterey Submarine Canyon on the large scale coastal circulation. Quantitative comparisons show the importance of non-hydrostatic effects in the coastal ocean simulation. The non-hydrostatic model predicts the vertical structure much more accurately.