A Three-Dimensional Fully Nonlinear Model in Curvilinear Coordinates for Simulating Waves Interaction with a Bottom-Mounted or Partially-Submerged Fixed Cylindrical Structure
Chen, Yu Hsiang
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This dissertation presents a three-dimensional fully nonlinear wave model developed to simulate solitary waves propagating in straight or curved channels and interactions bottom mounted or partially submerged structures. The three-dimensional Laplace equation and fully nonlinear boundary conditions are solved numerically by the finite difference method. In order to have the computational grids fit closely to the curved structural boundaries and the time varying free surface for numerical advantage, the transient three-dimensional curvilinear coordinate transformation technique is adopted to convert the original governing equation and boundary conditions in Cartesian coordinates into the curvilinear coordinate based formulations. The effects of grid size and time step on the accuracy and convergence of the present numerical model are examined and discussed by simulating a solitary wave freely propagating in a straight rectangular channel. Then, the feature of the curvilinear coordinate transformation is tested by modeling the case of a solitary wave propagating in a 180° curved channel. After comparing with the results obtained from the generalized Boussinesq (gB) two-equation model, this three-dimensional model can produce stable and accurate predictions on nonlinear waves propagation in a channel with irregular boundary. The present three-dimensional model is extended to solve the wave and structure interaction problems. One of the cases is a solitary wave impinging a bottom mounted and surface piercing vertical cylinder. The results obtained from the present three-dimensional model shows a reasonable agreement with the experimental measurements and those calculated from the gB model. The other case is a solitary wave interacting with a partially submerged and fixed floating cylinder. Laboratory tests for a solitary wave passing through a partially immersed and fixed floating cylinder were conducted to verify the present three-dimensional model performance. The numerical results of the present model match well with the experimental measurements. It is demonstrated through these comparisons that the present three-dimensional fully nonlinear wave model can provide reliable predictions on wave evolution and loading for a solitary wave interacting with selected cylindrical structures.