An unstructured finite volume numerical scheme for extended Boussinesq-type equations for irregular wave propagation

The interplay between low and high frequency waves is groundwork for the near-shore hydrodynamics for which Boussinesq-type (BT) equations are widely applied dur- ing the past few decades to model the waves’s propagation and transformations. In this work, the TUCWave code is vali- dated with respect to the propagation, transformation, breaking and run-up of irregular waves. The main aim is to investigate the ability of the model and the breaking wave parametriza- tions used in the code to reproduce the nonlinear properties of the waves in the surf zone. The TUCWave code numer- ically solves the 2D BT equations of Nwogu (1993) on un- structured meshes, using a novel high-order well-balanced fi- nite volume (FV) numerical scheme following the median dual vertex-centered approach. The BT equations are recast in the form of a system of conservation laws and the conservative FV scheme developed is of the Godunov-type. The approxi- mate Riemann solver of Roe for the advective fluxes is utilized along with a well-balanced topography source term upwinding and accurate numerical treatment of moving wet/dry fronts. The dispersion terms are discretized using a consistent, to the FV framework, discretization and the friction stresses are also included. High-order spatial accuracy is achieved through a MUSCL-type reconstruction technique and temporal through a strong stability preserving Runge-Kutta time stepping. Wave breaking mechanism have also been developed and incorpo- rated into the model. TUCWave code is applied to bench- mark test cases and real case scenarios where the shoaling and breaking of irregular waves is investigated