In the present study, a fifth-order weighted essentially non-oscillatory (WENO) scheme was built for solving the surface-capturing level-set equation. Combined with the level-set equation, the three-dimensional Reynolds averaged Navier-Stokes (RANS) equations were employed for the prediction of nonlinear wave-interaction and wave-breaking phenomena over sloping beaches. In the level-set finite-analytic Navier-Stokes (FANS) method, the free surface is represented by the zero level-set function, and the flows are modeled as immiscible air-water two phase flows. The Navier-Stokes equations for air-water two phase flows are formulated in a moving curvilinear coordinate system and discretized by a 12-point finite-analytical scheme using the finite-analytic method on a multi-block over-set grid system. The Pressure Implicit with Splitting of Operators / Semi-Implicit Method for Pressure-Linked Equation Revised (PISO/SIMPLER) algorithm was used to determine the coupled velocity and pressure fields. The evolution of the level-set method was solved using the third-order total variation diminishing (TVD) Runge-Kutta method and fifth-order WENO scheme. The accuracy was confirmed by solving the Zalesak's problem. Two major subjects are discussed in the present study. First, to identify the WENO scheme as a more accurate scheme than the essentially non-oscillatory scheme (ENO), the characteristics of a nonlinear monochromatic wave were studied systematically and comparisons of wave profiles using the two schemes were conducted. To eliminate other factors that might produce wave profile fluctuation, different damping functions and grid densities were studied. To damp the reflection waves efficiently, we compared five damping functions. The free-surface elevation data collected from gauges distributed evenly in a numerical wave tank are analyzed to demonstrate the damping effect of the beach. Second, as a surface-tracking numerical method built on curvilinear coordinates, the level-set RANS model was tested for nonlinear bichromatic wave trains and breaking waves on a sloping beach with a complex free surface. As the wave breaks, the velocity of the fluid flow surface became more complex. Numerical modeling was performed to simulate the two-phase flow velocity and its corresponding surface and evolution when the wave passed over different sloping beaches. The breaking wave test showed that it is an efficient technique for accurately capturing the breaking wave free surface. To predict the breaking points, different wave heights and beach slopes are simulated. The results show that the dependency of wave shape and breaking characteristics to wave height and beach slope match the results provided by experiments.

In the present study, a fifth-order weighted essentially non-oscillatory (WENO) scheme was built for solving the surface-capturing level-set equation. Combined with the level-set equation, the three-dimensional Reynolds averaged Navier-Stokes (RANS) equations were employed for the prediction of nonlinear wave-interaction and wave-breaking phenomena over sloping beaches. In the level-set finite-analytic Navier-Stokes (FANS) method, the free surface is represented by the zero level-set function, and the flows are modeled as immiscible air-water two phase flows. The Navier-Stokes equations for air-water two phase flows are formulated in a moving curvilinear coordinate system and discretized by a 12-point finite-analytical scheme using the finite-analytic method on a multi-block over-set grid system. The Pressure Implicit with Splitting of Operators / Semi-Implicit Method for Pressure-Linked Equation Revised (PISO/SIMPLER) algorithm was used to determine the coupled velocity and pressure fields. The evolution of the level-set method was solved using the third-order total variation diminishing (TVD) Runge-Kutta method and fifth-order WENO scheme. The accuracy was confirmed by solving the Zalesak's problem. Two major subjects are discussed in the present study. First, to identify the WENO scheme as a more accurate scheme than the essentially non-oscillatory scheme (ENO), the characteristics of a nonlinear monochromatic wave were studied systematically and comparisons of wave profiles using the two schemes were conducted. To eliminate other factors that might produce wave profile fluctuation, different damping functions and grid densities were studied. To damp the reflection waves efficiently, we compared five damping functions. The free-surface elevation data collected from gauges distributed evenly in a numerical wave tank are analyzed to demonstrate the damping effect of the beach. Second, as a surface-tracking numerical method built on curvilinear coordinates, the level-set RANS model was tested for nonlinear bichromatic wave trains and breaking waves on a sloping beach with a complex free surface. As the wave breaks, the velocity of the fluid flow surface became more complex. Numerical modeling was performed to simulate the two-phase flow velocity and its corresponding surface and evolution when the wave passed over different sloping beaches. The breaking wave test showed that it is an efficient technique for accurately capturing the breaking wave free surface. To predict the breaking points, different wave heights and beach slopes are simulated. The results show that the dependency of wave shape and breaking characteristics to wave height and beach slope match the results provided by experiments.