Mathematical modelling and numerical solution of run-up waves on a sloping beach extended with an artificial bottom

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University of Dar es Salaam
Beaches in Tanzania are constantly dynamic resulting to an enormous loss of property and investments, flora and fauna and even the natural beauty. Such a phenomenon requires attention and action to rectify it. This study has developed a model that focuses on the swash zone as part of a bigger study intended to get the general understanding of the beach erosion problems Tanzania is facing. The model comprises of two dimensional depth-averaged nonlinear shallow water equations (NSWE) with forcing teens. For the numerical implementation of the model an artificial viscosity term has been introduced. The computational domain is extended with an artificial layer of constant depth, (ε) which alleviates a great complication of modeling swash zone flows characterized by both intermittency and occurrences of motions with different scales. Several assumptions are considered and the model is solved and simulated using Finite Element Laboratory (FEMLAB) commercial software. A solution (w) has been found which permits an evaluation of flows on a sloping beach that is cut-off at a level below that of a maximum run-up creating a flat artificial distance (Lo). Simulations have been done for both alongshore bottom independent and dependent cases. In both cases it has been shown that the solution converges as ε- O and also we found the smallest distance Lo which can be altered without significantly changing the solution. Observations on simulations fit very well with the general knowledge and experimental/field results. The simulation results can directly be an input to the sediment transport and profile evolution modules not only to Tanzania but also to other areas with similar problems. Finally, we are convinced that the results presented in this thesis can be very helpful and guiding to other researchers from other disciplines and to decision makers.
Available in print form, East Wilbert Africana Collection, Dr. Wilbert Chagula Library, Class mark (THS EAF QA297.M7)
Numerical solution, Mathematical model, Wave equation
Mtega, N. A. L(2005)Mathematical modelling and numerical solution of run-up waves on a sloping beach extended with an artificial bottom, Master dissertation, University of Dar es salaam, Dar es Salaam