Abstract
Accurate and efficient numerical wave generation and absorption of two-dimensional nonlinear periodic waves traveling on a steady, uniform current were carried out in a potential, fully nonlinear numerical wave tank. The solver is based on the Βoundary Εlement Μethod (ΒΕΜ) with linear singularity distributions and plane elements and on the mixed Eulerian–Lagrangian formulation of the free surface equations. Wave generation is implemented along the inflow boundary by imposing the stream function wave solution, while wave absorption at both end-boundaries is effectively treated by introducing absorbing layers. On the absorbing beach side, the outflow boundary condition is modified to ensure that the solution accurately satisfies the dispersion relation of the generated waves. The modification involves a free-parameter that depends on the mass flux through the domain and is determined through a feedback error-correction loop. The developed method provides accurate time domain wave solutions for shallow, intermediate, and deep water depths of high wave steepness (wave heights up to 80% of the maximum value) that remain stable for 150 wave periods. This also holds in case a coplanar or opposing uniform current of velocity up to 20% of the wave celerity interacts with the wave.
Highlights
Over the years, the design of offshore structures, such as platforms and more recently wind and wave energy plants, has been mainly based on linear hydrodynamic theory
A stream function periodic wave solution is matched along the inflow boundary with wave height H = 1.905 cm and period T = 2.02 s
A fully nonlinear potential numerical wave tanks (NWT) was formulated based on the Boundary Element Method, with plane elements carrying linearly distributed singularities, and on the mixed Eulerian–Lagrangian formulation of the free surface equations
Summary
The design of offshore structures, such as platforms and more recently wind and wave energy plants, has been mainly based on linear hydrodynamic theory. They used a fully nonlinear NWT based on higher-order BEM and generated zero mass flux SF waves In their implementation, the inflow vertical boundary was moved in the horizontal direction through an iterative procedure, in order to deal with the poor resolution of the surface panels near the inflow boundary due to drift phenomena. The present work investigates the numerical and modeling aspects appearing in potential NWTs and aims at (a) accurate and stable numerical generation of periodic waves with very high wave steepness at a wide water depth regime, (b) modeling of the nonlinear wave–current interaction, and (c) effective wave absorption at the open boundary on the beach side, without affecting the nonlinear dispersion relation of the generated waves In this regard, the wave generation, propagation, and absorption of periodic waves with very high wave steepness, interacting with a steady uniform current, are considered in a fully nonlinear potential BEM-based NWT, using piecewise linear singularity. The time-varying integration constant appearing in the Bernoulli equation was eliminated, leading to a proper redefinition of φ(x; t)
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