Modelling wave transformations using extended mild-slope equation and the radial basis function colloaction method

Abstract

In this study, the extended mild-slope equation is modelled over different topogra phies using the Radial Basis Function Collocation Method. In the numerical model, the equation preserved its elliptic form and two related new boundary conditions are presented as combined generating transmitting boundary condition and transmitting boundary condition. Time integration of the model is handled by Stoermer’s method that rarely encountered in numerical analysis of wave models. In the first part, bound ary conditions are tested in constant depth domain using the extended mild-slope equa tion for wave propagation. In the second part, propagation of wave is modelled over a plane slope using two different RBFs at the same time for approximating different parameters. Subsequently, performance of the extended mild-slope equation is analyzed for sudden bathymetry changes using negative step, positive step and symmetric trench as test cases. The results of the tests show acceptable agreement with previous researches and analytical solutions. Lastly, transformation of waves are tested using the EMSE for 3 different complex bathymetries generated by combining the bathyme tries of the previous test cases. The predicted shoaling, reflection and transmission characteristics in the wave profiles are obtained from the numerical results.