Development of a Non-hydrostatic Model for Simulating Free-surface Waves
Date Issued
2009
Date
2009
Author(s)
Young, Chih-Chieh
Abstract
A higher-order 3D non-hydrostatic model in a sigma-coordinate system is developed for simulating free-surface wave propagation from deep to shallow waters. The model using an implicit finite difference scheme on a staggered grid simultaneously solves the unsteady Navier–Stokes equations and the free-surface boundary condition. A higher-order top-layer pressure treatment is proposed to resolve dispersive wave propagation. To capture non-linear waves, a 4th-order spatial discretization is utilized to approximate the large horizontal pressure gradient. Based on a domain decomposition method, the 3D system matrix is decomposed into a series of 2D vertical plane problems. An efficient direct solver is developed to solve the resulting block hepta-diagonal sub-system matrix. Model’s characteristics including linear wave dispersion and non-linearity are critically examined. The model is then applied to examine a range of free-surface wave problems including the co-existence of waves and currents, non-linear deep-water wave group and near-shore wave propagating over irregular bottom. Features of wave-current, wave-wave, and wave-bottom interactions are carefully discussed. Overall, good agreement between the model results and experimental data shows that the newly developed non-hydrostatic model using a few vertical layers (e.g. 2-5) is capable of accurately and efficiently resolving various wave phenomena.
Subjects
non-hydrostatic pressure
sigma co-ordinate
dispersion
non-linearity
wave-current interactions
wave-wave interactions
wave-bottom interactions
Type
thesis
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