Investigation of finite volume methods for free surface flows with focus on the numerical description of the air-water interface

The existing solution procedure for two phases in OpenFOAM suffers from unphysical velocity oscillations at the free surface. We aimed to solve this by imposing the boundary conditions directly on the free surface. We have taken the first step towards a new two-phase solution method by first addressing the water phase alone. It is a free surface modelling method based on merging concepts from two existing methods: (1) A single-phase free surface method and (2) the solution method in OpenFOAM. The underlying motivation for the study was to enable more accurate estimation of the wave induced load distributions from wave crest impacts on offshore structures. This requires an accurate prediction of the kinematics near the free surface. We present a solution method with boundary conditions directly on the free surface, thereby the name: Direct Surface Description (DSD). Additionally it is the first time that the isoAdvector algorithm is combined with a single phase free surface method. A still water level simulation is presented to illustrate the unphysical behaviour of the existing solvers and validate the behaviour of the DSD method. The second test case is a moderately steep stream function wave in intermediate water depth. The DSD method is validated and compared to the existing solution methods of OpenFOAM (interFoam and interIsoFoam) by presenting a detailed comparison of surface elevations and velocity profiles. This is followed by a convergence study of the error of the wave height, the max and mean velocity over the depth and the crest phase shift. Additionally the effect of the Courant–Friedrichs–Lewy (CFL) number is studied. The stream function wave case demonstrates that the DSD method accurately predicts the free surface elevation and velocity fields without free surface undulations or oscillatory velocity fields. The convergence study shows the increased accuracy of the DSD method. The solitary wave case shows that the DSD method provides accurate velocity fields and surface elevations for horizontally elongated cells. The shoaling solitary wave demonstrates that the DSD solvers predicts correct shoaling to the point of breaking. Furthermore, these simulations illustrate that they can handle the post breaking region, which is challenging for numerical solvers. A standing wave simulation studies the evolution of the wave over 20 periods. The wave height increases dramatically for the explicit DSD solver, which indicates that there is an inconsistency in the coupling between the free surface advection and the pressure-velocity coupling. The classical dam break case further validates both solvers. Finally the focused wave simulation shows that the developed DSD method works in 3D with a simulation of a wave breaking impact on a vertical cylinder. For the focused wave simulation a new static piston
wave maker boundary condition has been implemented for the focused wave generation using a piston position signal. To conclude, the new DSD method provide a solution to the problem with unphysical velocities at the free surface. The DSD solvers provides accurate results for the presented test cases and they can handle complex free surface flows in a 3D simulation. They form a solid base for extending the solvers to two phase flows and future study of wave induced forces on offshore structures.