Wave Model and Watercraft Model for Simulation of Sea State

Abstract: The problem of real-time simulation of ocean surface waves, ship movement and the coupling in between is tackled, and a number of different methods are covered and discussed. Among these methods, the finite volume method has been implemented in an attempt to solve the problem, along with the compressible Euler equations, an octree based staggered grid which allows for easy adaptive mesh refinement, the volume of fluid method and a variant of the Hyper-C advection scheme for compressible flows for advection of the phase fraction field. The process of implementing the methods that were chosen proved to be tricky in many ways, as they involve a large number of advanced topics, and the implementation that was implemented in this thesis work suffered from numerous issues. There were for example problems with keeping the interface intact, as well as a harsh restriction on the time step size due to the CFL condition. Improvements required to make the method sustainable for real-time applications are discussed, and a few suggestions on alternative approaches that are already in use for similar purposes are also given and discussed. Furthermore, a method for compensating for gain/loss of mass when solving the incompressible flow equations with an inaccurately solved pressure Poisson equation is presented and discussed. A momentum conservative method for transporting the velocity field on staggered grids without introducing unnecessary smearing is also presented and implemented. A simple, physically based illumination model for sea surfaces is derived, discussed and compared to the Blinn–Phong shading model, although it is never implemented. Finally, a two-dimensional partial differential equation in the spatial domain for simulating water surface waves for mildly varying bottom topography is derived and discussed, although it is deemed to be too slow for real-time purposes and is therefore never implemented.