The boundaries of numerical domains for free-surface wave simulations with marine structures generate spurious wave reflection if no special measures are taken to prevent it. The common way to prevent reflection is to use dissipation zones at the cost of increased computational effort. On many occasions, the size of the dissipation area is considerably larger than the area of interest where wave interaction with the structure takes place. Our objective is to derive a local absorbing boundary condition that has equal performance to a dissipation zone with lower computational cost. The boundary condition is designed for irregular free-surface wave simulations in numerical methods that resolve the vertical dimension with multiple cells. It is for a range of phase velocities, meaning that the reflection coefficient per wave component is lower than a chosen value, say 2%, over a range of values for the dimensionless wave number kh. This is accomplished by extending the Sommerfeld boundary condition with an approximation of the linear dispersion relation in terms of kh, in combination with vertical derivatives of the solution variables. For this article, the boundary condition is extended with a non-zero right-hand side in order to prevent wave reflection, while, at the same time, at the same boundary, generating waves that propagate into the domain. Results of irregular wave simulations are shown to correspond to the analytical reflection coefficient for a range of wave numbers, and to have similar performance to a dissipation zone at a lower cost.

Wave loads on crest walls on top of rubble mound structures determine the size of these crest walls. For the design of crest walls some design guidelines exist, but their validity is limited to particular designs of the cross section (berm, no berm, toe, armour layout, protruding crest element, etc). The present work addresses the validation of OpenFoam/waves2Foam for the prediction of integrated forces on crest wall elements against a new set of experimental data in order to obtain a numerical model that can be applied for a wider field of application than the existing empirical guidelines. One key concern for the accurate modelling of wave loads is the spurious entrapment of air between the water surface and structural elements. The solution developed for this problem is a boundary condition that allows for air ventilation, while enforcing a predefined head loss characteristic. Compared to the existing technique of introducing small meshed tubes through the structure, the new method does not lead to excessive time-step limitations and is therefore more efficient (a practical case was accelerated by a factor 20). The new boundary condition is validated against experimental data of forces on bridge decks with girders. Subsequently, the numerical model is validated against experimental data for loads on crest wall elements from new experiments conducted in a wave flume. The comparison between numerical and experimental data is made both in the time domain and as probability of exceedance. Special emphasis is given to the openness of the faces of the crest wall to mimic the effect of mixing of water and air during the wave impact. Finally, the validated model is applied to evaluate the forces on crest walls as a function of the elevation of the crest wall with respect to the still-water level. This effect is of interest, since the level of the crest wall element is only tested to a limited extent in laboratory experiments and the bottom face was mainly wetted or submerged during these tests (existing empirical formulations). The numerical results are compared to an empirical design formulation [Pedersen, 1996] and conclusions on the general applicability of this particular empirical design formulation are presented. The effect of the shape of the wave spectrum on the resulting forces is investigated in a preliminary fashion.

COMFLOW is a general 3D free-surface flow solver. The main objective in this paper is to extend the solver with a permeable flow model to simulate wave interaction with rubble-mound breakwaters. The extended Navier-Stokes equations for permeable flow are presented and we show the discretization of these equations as they are implemented in COMFLOW. An analytical solution for the reflection coefficient of a permeable structure is derived and the numerical model is compared to the solution. In addition, a validation study has been performed, in which we compare the numerical results with an experiment. In the experiment, pressures and surface elevations are measured inside a permeable structure. The measurements are represented well by the simulation results. At the end, a 3D application of the model is shown.

An extensive data set of waves propagating over a shoal on a beach has been obtained from measurements in a three-dimensional physical model. The data set has been used to validate the two-dimensional Boussinesq-type wave model TRITON. In particular the performance of the implemented wave-breaking model has been investigated. Since the unique data set contains a variety of wave regimes, also the modeling of other wave aspects, such as linear dispersion and shoaling, as well as nonlinear wave-wave interaction can be verified.

A procedure is presented for the dynamic handling of the boundaries of Boussinesq-type wave models that enables to control the reflection properties. The main purpose of the procedure is the reduction of spurious reflections at open boundaries. The procedure also allows, however, the modeling of partial reflection at closed boundaries. The approach chosen takes into account the effect of wave direction, wave period, and wave height, in order that irregular waves, waves at arbitrary angles, and steep waves can all be handled properly. An innovative aspect of the developed method is that it can equally well be used for strongly dispersive waves, since besides the angle of outgoing waves also the celerity is determined dynamically. The results presented demonstrate the feasibility of the approach; reflection coefficients of only about 1% are obtained for regular waves, varying angle, period, as well as steepness.

The Boussinesq-type modeling concept provides an adequate and efficient means to describe wave dynamics in coastal regions. They are an extension of the depth-averaged shallow-water model and include the propagation of short waves as well as nonlinear effects. The Boussinesq-type model applied in this paper has been developed to obtain an accuracy sufficient for practical purposes within limited computing times. We present the extension of this model with a 2-D wave breaking model based on a combination of the eddy viscosity concept and the surface roller concept. The combination has a number of features that makes it suitable for nearshore applications. Mass and momentum are strictly conserved while the wave breaking model only dissipates energy, which is in agreement with physical laws. The results and the comparison with experiments under very different wave conditions demonstrate the good performance of the model.

There are numerous ways to derive a system of 2D Boussinesq-type wave equations from the 3D potential flow equation with free-surface boundary conditions. This freedom in design is exploited here to derive a Boussinesq-type model that has a number of unique properties. It describes the depth-integrated transport of mass and momentum in strictly conservative form. Its compact formulation is independent of the vertical reference level and allows for an efficient implementation. The model is complemented with absorbing boundary conditions that dynamically take into account the average celerity and direction of both the incoming and the outgoing wave. The model is validated by means of a number of standard test cases.