Wave Absorption

Active Wave Absorption

Active wave absorption is included in the model, following the methodology developed by Schäffer & Klopman (2000). Although this method is based on shallow water linear theory, its performance is very good even if this condition is not fulfilled. It identifies the waves that reach a boundary and then absorbs them to avoid their reflection. The main advantage of this kind of absorption is that it prevents the energetic and mean water levels to increase unbounded, while adding no significant computational cost to the model.

This method also allows for an accurate wave generation simultaneously with the wave absorption for both the Dirichlet and the moving boundary conditions. The first step is to calculate the difference between the expected (target) free surface and the one measured in the model. Then the wave maker velocity is modified so as to generate the target wave and at the same time to cancel out the wave to be absorbed. Consequently, the correction of the velocity must be added to the target velocity of the generated wave. Finally if we are using the moving paddle another correction has to be applied to the position of the wave maker. The modified position is calculated by integrating the corrected velocity and adding it to the target displacement.

Active wave absorption can be applied alone on a boundary, to act like an open boundary condition for waves.

The video below shows wave generation on the right boundary, and active wave absorption on the left (moving) one.

Passive Wave Absorption

The passive wave absorption method consists of a region in which a dissipation model is defined. This method was implemented to work together with the source function wave generation, and now that the other wave generation and active wave absorption methods are implemented as well it is less likely to be used. Its main goal is to avoid the reflections on the boundary, as waves generated by the source function travel in the two directions,  but it also dissipates any other incident waves from the zone of interest.

This sponge layer is implemented following Israeli & Orszag (1981) formulation. The optimal length of this area is around 2 wave lengths, and allows the model to run for longer periods without the effect of inconvenient reflections. This region placed behind the source function area is an additional domain, hence the resultant mesh is significantly larger. This causes an even more expensive time cost.