In this work, periodic lateral boundaries are developed in a time dependent mild-slope equation model, MILDwave, for the accurate generation of regular waves and irregular long and short crested waves in any direction. A single wave generation line inside the computational domain is combined with periodic lateral boundaries. This generation layout yields a homogeneous and thus accurate wave field in the whole domain in contrast to an L-shaped and an arc-shaped wave generation layout where wave diffraction patterns appear inside the computational domain as a result of the intersection of the two wave generation lines and the interaction with the lateral sponge layers. In addition, the performance of the periodic boundaries was evaluated for two different wave synthesis methods for short crested waves generation, a method proposed by Miles and a method proposed by Sand and Mynett. The results show that the MILDwave model with the addition of periodic boundaries and the Sand and Mynett method is capable of reproducing a homogeneous wave field as well as the target frequency spectrum and the target directional spectrum with a low computational cost. The overall performance of the developed model is validated with experimental results for the case of wave transformation over an elliptic shoal (Vincent and Briggs shoal experiment). The numerical results show very good agreement with the experimental data. The proposed generation layout using periodic lateral boundaries makes the mild-slope wave model, MILDwave, an essential tool to study coastal areas and wave energy converter (WEC) farms under realistic 3D wave conditions, due to its significantly small computational cost and its high numerical stability and robustness.
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