Radial Basis Function Collocation Models for Water Wave Propagation over a Submerged Breakwater

Abstract

In this study, two different numerical models are developed using the radial basis function collocation method (RBFCM) for the waves propagating over variable bathymetry.  For the verification and validation of the models, submerged breakwater test, present in the literature, is used. One of the models is based on the Navier-Stokes equations where the fluid is assumed to be viscous, incompressible and is of constant density. Also, it is assumed that the flow is unsteady and the turbulent effects are neglected. And for the other model, it is assumed that the fluid is inviscid, incompressible and is of constant density while the flow is assumed to be unsteady and irrotational. On the surface, fully nonlinear forms of the free surface boundary conditions are implemented using the semi-Lagrangian approach. Multiquadric radial basis functions (MQRBF) are used for the approximation of the unknown parameters. Since each of the models requires the solution of an elliptic boundary value problem, extra collocation centers are defined outside the problem domain in the neighborhood of the boundary centers to define both the boundary condition and the governing equation at a boundary center for better accuracy and stability. It is observed that the results of the both models are in agreement with the laboratory test results.

Keywords

• water wave propagation,radial basis function collocation,numerical modelling,Navier-Stokes equations,Laplace Equation

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