ABSTRACT
5.1 Introduction
This chapter describes finite element methods often employed in coastal hydraulics in general and highlights a characteristic-based Galerkin method suited for advection-dominated problems (Chau et al. 1991; Chau 1992b). A two-step algorithm is also presented which significantly reduces the computational cost. It is shown for the 1-D scalar advection equation that the time-discretized equation can also be obtained by following a characteristics approach. The governing hydrodynamic and mass transport equations are written in conservative form, in order to exploit the full power for the numerical technique. An error analysis of the scheme using linear elements for spatial discretization is given for the one-dimensional advection-dominated equation. Remarks on advantages and disadvantages of the characteristic-Galerkin method are then made. Two applications of this robust finite element model in engineering practice have been attempted. The model is first applied to compute tidal current and advective mass transport in Tolo Harbour, Hong Kong. A scalar pollutant is released at the Yung Shue Au fish culture zone in Three Fathoms Cove. The flushing rates of semi-enclosed bays in the harbour are determined numerically via a solution of the full equations with a realistic tidal boundary condition and over half spring-neap cycle. The model is also applied to study the effect of proposed massive reclamation under the Hong Kong Port and Airport Development Strategy (PADS) project on tidal current in Victoria Harbour, Hong Kong, which is a more difficult task since there are two open boundaries.
