A particle finite element method applied to long wave run-up

This paper presents a Lagrangian-Eulerian finite element formulation for solving fluid dynamics problems with moving boundaries and employs the method to long wave run-up. The method is based on a set of Lagrangian particles which serve as moving nodes for the finite element mesh. Nodes at the moving shoreline are identified by the alpha shape concept which utilizes the distance from neighbouring nodes in different directions. An efficient triangulation technique is then used for the mesh generation at each time step. In order to validate the numerical method the code has been compared with analytical solutions and a preexisting finite difference model. The main focus of our investigation is to assess the numerical method through simulations of three-dimensional dam break and long wave run-up on curved beaches. Particularly the method is put to test for cases where different shoreline segments connect and produce a computational domain surrounding dry regions. Copyright (c) 2006 John Wiley & Sons, Ltd.