Proceedings of MekIT'15 Eighth National Conference on Computational Mechanics. 2015, 275-294
We present an overview of the continuous and discontinuous Galerkin finite element methods (CG-FEM, DG-FEM) for numerical solution of the transport equation and show how the Navier-Stokes equations can be solved with CG-FEM in both a coupled and segregated manner. We show convergence of the implemented Navier-Stokes solvers for single-phase ows on the well known Taylor-Green vortex and also show how the volume of uid (VOF) method for tracking the interface between two uids can be implemented in DG-FEM. Our work is aimed towards creating a method for looking at the impact forces from water waves on structures and comments are made on how to evolve the presented solution methods into a two-phase solver that can handle the physics involved in highly non-linear free surface simulations.