A new numerical model for simulations of wave transformation, breaking and long-shore currents in complex coastal regions

In this paper, we propose a model based on a new contravariant integral form of the fully nonl inearBoussinesq equations in order to simulate wave transformation phenomena, wave breaking, and nearshorecurrents in computational domains representing the complex morphology of real coastal regions. The afore-mentioned contravariant integral form, in which Christoffel symbols are absent, is characterized by the factthat the con tinuity equation does not include any dispersive term. A procedure developed in order to correcterrors related to the difficult ies of numerically satisfying the metric identities in the numerical integration offully nonlinear Bous sinesq equation on generalized boundary-conforming grids is presented. TheBoussinesq equation system is numerically solved by a hybrid finite volume–finite difference scheme.The proposed high-order upwind weighted essentially non-oscillatory finite volume scheme involves anexact Riemann solver and is based on a genuinely two-dimensional reconstruction procedu re, which usesa convex combination of biquadratic polynomials. The wave breaking is represented by discontinuities ofthe weak solution of the integral form of the nonlin ear shallow water equations.The capacity of the proposed model to correctly represent wave propagation, wave breaking, and wave-induced currents is verified against test cases present in the literature. The results obtained are comparedwith experimental measures, analytical solutions, or alternative numerical solutions.