Optimizing wave generation and wave damping in 3D-flow simulations with implicit relaxation zones

In finite-volume-based flow simulations with free-surface waves, wave reflections at the domain boundaries can cause substantial errors in the results. 'Implicit relaxation zones' can be used to minimize these reflections, but only if the relaxation zone's case-dependent parameters are optimized. This work proposes an analytical approach for optimizing these parameters. The analytical predictions are compared against results from 2D-flow simulations for different water depths, wave steepnesses, flow solvers, and relaxation functions, and against results from 3D-flow simulations with strongly wave-reflecting bodies subjected to nonlinear free-surface waves. The present results demonstrate that the proposed approach satisfactorily predicts both the optimum parameter settings and the upper-limit for the corresponding reflection coefficients C-R. When optimized as proposed, simulation results for C-R were mostly below or equal to the analytical predictions, but never more than 2.2% larger. Therefore, the proposed approach can be recommended for engineering practice. Furthermore, it is shown that implicit relaxation zones can be considered as a special-case of 'forcing zones', a family of approaches which includes absorbing layers, damping zones and sponge layers amongst others. The commonalities and differences between these approaches are discussed, including to which extent the present findings are applicable to these other approaches and vice versa.