| Summary: | The shallow water equations have been solved numerically using the Galerkin finite element method. Flow problems which can be classified as one-dimensional and two-dimensional are investigated. Two differing types of integration procedure (Gaussian Quadrature scheme and a mixed quadrature scheme involving both Gaussian Quadrature and Simpson's Rule) are examined to determine the most efficient way of obtaining the finite element solutions. The mixed quadrature scheme is shown to be a faster but less accurate process than the Gaussian scheme. The numerical results from the one-dimensional models are initially tested by comparison with the known analytic solutions for a straight channel and a wedge-shaped channel. Solutions from numerical models show good agreement with the analytic solutions. The one-dimensional models are also used to simulate the M<SUB>2</SUB> tide in the Bristol Channel. The results are in good agreement with observed field data. The two-dimensional models are tested against analytic solutions for a straight canal and an open coastal embayment with a variety of bottom topographies. The numerical results are in good agreement with the analytic solutions. Finite element solutions are found for real situations, in particular the area around Lundy Island within the Bristol Channel and in the Bristol Channel itself. The numerical solutions are compared with the observed field data. The two-dimensional numerical models produce solutions which are in good agreement with observed field data. An analysis of the eddy formation around Lundy Island shows that these features, which were first observed in satellite imagery, are predicted by the two-dimensional numerical models. Coriolis force is shown to be important in the formation of the island wake. The one-dimensional numerical models are less successful in predicting the observed field data than the two-dimensional numerical models but the former are very efficient in terms of computer time and also provide a good prediction of water levels and elevation phase lags.
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