A non-hydrostatic numerical model for simulating regular wave breaking and surf-swash zone motions

In the present study, a non-hydrostatic two-dimensional vertical model has been developed to simulate the breaking of regular waves and surf-swash zone motions on a sloping beach. The objective of the present study was to estimate parameters at depth. The governing equations, based on the pressure-correction projection method, were solved in two main phases. In the initial phase, intermediate velocities were acquired through the resolution of advection-diffusion and explicit dynamic pressure gradient terms within the momentum equations, employing a time-splitting technique. To ensure local momentum conservation and solution monotonicity, modifications were made to the governing equations and the solution approach. In the second phase, through the substitution of intermediate velocities and the corrected pressure gradient term from the momentum equations into the continuity equation, with the elimination of velocities, a Poisson pressure-correction equation was derived. In the discretization stage, an innovation was proposed to compute horizontal velocities at the locations where vertical velocities are present, significantly reducing computational costs. The equation was then converted into a system of linear equations, which was solved implicitly. Comparisons between numerical results and experiments concerning plunging and spilling breakers reveal that the developed model satisfactorily simulates the outcomes.