Modelling of long wave propagation 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 bepresented. An efficient meshless numerical scheme, which is an easily adaptable con-vergent new technique, based on the Radial Basis Functions Collocation Method hasbeen employed in the model. Long wave propagation model is developed using the non-linear shallow water equations which is applicable at different water depths, includingthe run-up regions. In the model, ow resistance can optionally be introduced throughthe bottom shear stress and the dispersion effect is neglected. From coastal and oceanengineering aspects, water wave propagation to coastal zones directly effects coastalmorphology. The obtained water velocity uxes and elevations which are an impor-tant parameter for the force on the structures can easily be tested by interdisciplinaryworks. A numerical model case study is presented. The method has proved itself tobe an efficient method in the sense of the programming effort and the computationtimes. Therefore the efficiency of the method in terms of programming effort can beattributed to the fact that collocation nodes are placed easily in the regular, irregu-lar and adjustable computation domains. Besides, reduced computation time is alsoan important issue about the efficiency of the models. Applying different RBF andtechniques were found to be a promising method for the long wave propagation andthe 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 modified by the help of RBF. RBFhas the advantages of meshless structure, convergent new technique which decreasescomputational time, easily formulated for hyperbolic, elliptic and parabolic problems.