Radial basis function model of navier - stokes equations for water waves

Abstract

In this study a numerical model using the radial basis function collocation method (RBFCM) is developed for water wave propagation described by the Navier-Stokes equations. For the test cases, two dimensional horizontal bottom tests and submerged breakwater test are performed and the results are verified with the expected solutions and the experiment results of Luth et al. (1994). The collocation configuration is implemented to change instantly depending on the evolution of the free surface so that a center close to the surface below a crest can be out of the defined collocation set at another instant if there is trough on the free surface. The projection method of Chorin (1968) is used to create an auxiliary equation from the continuity to compute for the pressure in the flow field and the resulting Poisson equation is modeled using the collocation on the boundary technique to obtain better accuracy with the definition of additional out of domain centers close to the boundary which makes it possible to define the governing equation as well as the boundary condition at a boundary collocation center. The model is developed using the advanced features provided by the recent programming languages so that it is extensible to account for more details in the flow field and also different solvers can be implemented for different type of flows and problems.