Student Posters Repository

Free surface problems are of great interest since, for example, one may be interested in how water waves will interact and affect ships and offshore structures so that they can be designed optimally. These problems are modeled by systems of time dependent partial differential equations. At each time step, the free surface changes according to certain nonlinear boundary conditions. Hence, the problem includes determining the time dependent domain, which is computationally expensive and mathematically challenging. In this poster, we present the solution to the linear free surface problem for irrotational flows which is modeled by Laplace’s equation. In order to discretize the problem, we apply Finite Element Methods (FEMs) in which a piecewise polynomial approximation to the solution is sought over a discretized domain. In particular, we apply a hybridizable discontinuous Galerkin method which, in general, results into a smaller linear system compared to other discontinuous FEMs. The implementation is done in the C++ library MFEM which allows parallel computing. We show two numerical results, one where the analytical solution is known, and another one where we simulate waves in a water tank.