Simulation of propagation and run-up of landslide-induced waves using meshless method

Abstract

A two-dimensional numerical model using radial basis functions (RBFs) and collocation points for solving partial differential equations (PDE) is presented in this study. This method is a general meshless method called RBF collocation method. The basic concept of RBF collocation method is to approximate the solution for a PDE as a linear combination of RBFs. The feature of this method requires neither the domain nor the boundary meshes. The main framework is developed by Wu and Chang (2011), and is applicable for solving moving boundary problems with free surface wave. Different from the conventional RBF collocation methods that usually malfunction in the seeking of partial derivatives around the boundaries, the present model resolved the problems by additionally requiring the satisfaction of the governing equations on boundaries. The model validation is performed by comparing the present results of the submarine landslide induced-wave with other numerical solutions, such as BIEM (Lynett and Liu, 2002), a high-order Boussinesq-type model (Furhman and Madsen, 2009). Fairly good agreements are observed. Finally, the landslide-induced wave propagation and shoreline motion on three plane slopes are also discussed.