Modelling of long wave proagation using the radial basis function collocation method

Abstract

In this thesis, the depth averaged equations of motion and continuity, satisfy- ing certain additional conditions on the boundaries for long wave propagation will be presented. An efficient meshless numerical scheme, which is an easily adaptable con- vergent new technique, based on the Radial Basis Functions Collocation Method has been employed in the model. Long wave propagation model is developed using the non- linear shallow water equations which is applicable at different water depths, including the run-up regions. In the model, ow resistance can optionally be introduced through the bottom shear stress and the dispersion effect is neglected. From coastal and ocean engineering aspects, water wave propagation to coastal zones directly effects coastal morphology. The obtained water velocity uxes and elevations which are an impor- tant parameter for the force on the structures can easily be tested by interdisciplinary works. A numerical model case study is presented. The method has proved itself to be an efficient method in the sense of the programming effort and the computation times. Therefore the efficiency of the method in terms of programming effort can be attributed to the fact that collocation nodes are placed easily in the regular, irregu- lar and adjustable computation domains. Besides, reduced computation time is also an important issue about the efficiency of the models. Applying different RBF and techniques were found to be a promising method for the long wave propagation and the run-up. Thus the philosophy of this study is to bring a more elaborate, advanced, living model in the future that can be updated and modi ed by the help of RBF. RBF has the advantages of meshless structure, convergent new technique which decreases computational time, easily formulated for hyperbolic, elliptic and parabolic problems.