# Validation

#### Wave generation and propagation

The wave generation implemented in DualSPHysics has been used for regular and random waves comparing the numerical results with theoretical solutions of water surface elevation and orbital velocities. A very simple test case has been designed, where a piston wave-maker generates waves in a tank that ends with a vertical wall. The bottom of the tank is fully horizontal and the water depth *d* is 0.27m. The generated waves are regular and irregular waves of wave height *H*=0.1m and wave period *T*=1.3s.

The water surface elevation was measured at x=2m from the wave paddle and the results were compared with theoretical solutions (Stokes 2^{nd} order). The orbital horizontal and vertical velocities were measured at 0.15m below the still water level. Figures show the water surface elevation and orbital velocities for the regular and irregular wave case. The results from the 35m long wave tank match the theoretical solution, proving that the waves are properly generated and there is no reflection. In the case of the 4m long wave tank the wave behaviour diverges from the theoretical one because of the wave reflection on both sides of the tank.

The model has now been defined to resemble the one described in the previous section (the same water depth and wave characteristics) with the difference that the vertical wall at the end of the wave tank is replaced by a dissipative beach (11.3º) or a “sponge” area. The sketches of the models with passive wave absorption systems are depicted in the figure. The idea now is to avoid reflection without using a large domain of 35m. Therefore we introduce these passive absorption systems in the 4m long wave tank. Figure also compares the theoretical (Stokes 2^{nd} order) and numerical water surface elevation measured at x=2m where cases with dissipative beach and “sponge” area are reported. The same results calculated for the orbital velocities are plotted and a good agreement is observed between numerical results and theoretical solutions.

A snapshot taken at t=22.2s in the numerical simulation with regular waves is shown; the case without absorption and a domain size of only 4m is depicted with both absorption configurations. The results confirm the effectiveness of the implemented absorption systems for monochromatic waves: the simulation without any absorption is far from being representative of monochromatic waves, as also discussed in the previous section.

More information in:

Altomare C, Suzuki T, Domínguez JM, Barreiro A, Crespo AJC, Gómez-Gesteira M. 2015. Numerical wave dynamics using Lagrangian approach: wave generation and passive & active wave absorption. Proceedings of the 10th SPHERIC International Workshop, Parma, Italy.