A Finite Volume Based Fully Nonlinear Potential Flow Model for Water Wave Problems

A new Fully Nonlinear Potential Flow (FNPF) numerical model has been developed for the simulation of nonlinear water wave problems. At each time step, the mixed boundary value problem for the flow field is spatially discretised by Finite Volume Method (FVM) and the kinematic and dynamic free surface boundary conditions are defined in a semi-Eulerian-Lagrangian form, which are used to update the wave elevation and velocity potential on the free surface. In the numerical model, waves are generated through a relaxation zone and absorbed by an artificial damping zone at the inlet and outlet of the numerical wave tank (NWT), respectively. Instead of a five-point smoothing technique, a more versatile fourth-order technique is developed to eliminate the possible saw-tooth instability at the free surface. Test cases with increasing complexities, such as wave generation and absorption, 2- and 3-Dimensional wave shoaling, and wave-cylinder interaction are simulated to assess its accuracy, convergence, and robustness. For all the cases considered, satisfactory agreements of free surface elevation and wave-induced forces against the experimental measurements and other existing numerical results are achieved. The developed numerical model fully utilises the existing functionalities in OpenFOAM and has the potential to provide an effective alternative to other FNPF based models for constructing a hybrid numerical wave tank model through its coupling with the multiphase flow models in OpenFOAM.