Surf Simulation with the Shallow Water Equations : Coupling of a surfer model to a shallow water wave

Sammanfattning: This thesis covers the subject of deriving and solving the system of partial differential equations known as the Shallow Water Equations (SWE), and coupling the solutions of this equation system to a simplified model of a surfer - or any floating object, with the right choice of parameters. The SWE are generally used to analyze fluid movement on shallow areas, such as ocean waves nearing the shore, and are derived from the Navier-Stokes equations and restricted to conservation of mass and momentum in a fluid. In this project the solution to these equations was made to yield a propagating wave profile. From the solution, the steepening behaviour and the slow propagation speed of shallow water waves are explained - properties that are necessary for wave surfing. The SWE was solved with the first order accurate finite volume scheme known as the Lax Friedrichs Method (LxF), and a surfable wave is created with a suitable set of initial- and boundary conditions parameter values. LxF is also derived from the discretization of the conservation form of the SWE. The solver can also handle a non-horizontal seabed - bathymetry, but does not take into consideration friction from the seabed. A "surfer" was created as a point mass acted on by three forces: hydrodynamic drag, gravity and buoyancy. The "surfer" is made to move realistically by simulating the effect of these forces and updating position and velocity of the surfer accordingly. The surfer is made to move along with the wave.