An Implicit Discontinuous Galerkin Finite Element Method for Water Waves

摘要

We discuss a new higher order accurate discontinuous Galerkin finite element method for non-linear free surface gravity waves. The algorithm is based on an arbitrary Lagrangian Eulerian description of the flow field using deforming elements and a moving mesh, which makes it possible to represent non-linear large amplitude waves. The novel feature of the algorithm is a coupled treatment of the free surface boundary condition and the domain discretization, which improves numerical stability.