Large-Scale Free-Surface Flow Simulations Using FEM

A parallel finite element fluid-structure interaction free-surface solver is developed for numerical simulation of water waves interacting with floating objects. In our approach, the governing equations are the Navier-Stokes equations written for two incompressible fluids. An interface function with two distinct values serves as a marker identifying the location of the interface. The numerical method is based on writing stabilized finite element formulations in an arbitrary Lagrangian-Eulerian frame. This allows us to handle the motion of the floating objects by moving the computational nodes. In the mesh-moving schemes, we assume that the computational domain is made of elastic materials. The linear elasticity equations are solved to obtain the displacements. In order to update the position of the floating object, the nonlinear rigid body dynamics equations are coupled with the governing equations of fluids and are solved simultaneously. The mooring forces are modeled using nonlinear cables and linear spring models. The finite element formulation is implemented on Cray X1.