Numerical treatment of wave breaking on unstructured finite volume approximations for extended Boussinesq-type equations

A new methodology is presented to handle wave breaking over complex bathymetries in extended two-dimensional Boussinesq-type (BT) models which are solved by an unstructured well-balanced finite volume (FV) scheme. The numerical model solves the 2D extended BT equations proposed by Nwogu (1993), recast in conservation law form with a hyperbolic flux identical to that of the Non-linear Shallow Water (NSW) equations. Certain criteria, along with their proper implementation, are established to characterize breaking waves. Once breaking waves are recognized, we switch locally in the computational domain from the BT to NSW equations by suppressing the dispersive terms in the vicinity of the wave fronts. Thus, the shock-capturing features of the FV scheme enable an intrinsic representation of the breaking waves, which are handled as shocks by the NSW equations. An additional methodology is presented on how to perform a stable switching between the BT and NSW equations within the unstructured FV framework. Extensive validations are presented, demonstrating the performance of the proposed wave breaking treatment, along with some comparisons with other well-established wave breaking mechanisms that have been proposed for BT models.