A generating‐absorbing boundary condition for dispersive waves

The detailed modeling of free‐surface waves and their interaction with bottom‐mounted or floating structures requires large computational resources, which is why efficient boundary conditions with low spurious reflection are desirable. The present work presents a review of existing generating‐absorbing boundary conditions (GABCs) for dispersive waves and their reflection characteristics. Hereafter, an adaptation of the classical Sommerfeld condition is proposed by using a depth‐varying coefficient to improve absorption efficiency over a range of wave numbers. An analytical model is proposed to analyse the reflection characteristics for both propagating and evanescent modes, and a considerable improvement in comparison to the Sommerfeld condition is documented over a broad frequency range (reflection coefficients below 5% for nondimensional wave numbers in the range [0, 10]). The new boundary condition is implemented in OpenFoam® (waves2Foam) and the functioning for regular, irregular, solitary, and phase‐focused waves is presented. A new generating‐absorbing boundary condition for dispersive, free‐surface waves is proposed, for which the reflection characteristics can be predicted and optimized as a preprocessing step. Test cases for regular, irregular, phase‐focused, and solitary waves verify the performance of the boundary condition: it can ensure reflection below 5% over a broad wave number range (from shallow to deep water) and outperforms the classical Sommerfeld condition. The model is implemented in OpenFoam® and released through the waves2Foam toolbox.