Generation of free-surface waves by localized source terms in the continuity equation

Wave reflections at the wave-maker are a common problem in experiments and simulations of free-surface flow around bodies in waves. To overcome this problem in numerical investigations, a new method for deep water wave generation is presented. The waves are created by introducing mass source terms in the governing equations for a small part of the solution domain. By positioning the wave-maker inside the solution domain, wave damping can be applied to all domain boundaries. Wave reflections from the solution domain boundaries can thus be eliminated in simulations. The formulation of the mass source terms and the influence of the shape and location of the source region, where the mass source terms are introduced, are investigated in two-dimensional (2D) flow simulations based on the Navier-Stokes equations. It is demonstrated that the wave-maker can produce regular and irregular waves scale-independently for wave height to length ratios of H/λ≤0.056. A simulation of constructive and destructive water wave interference illustrates that incident waves can pass through the wave-maker without significant reflection. The wave-maker can be easily implemented in most computational fluid dynamics codes based on the Navier-Stokes equations (such as Reynolds-averaged Navier-Stokes (RANS) or Euler equation solvers).