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We propose an integral form of the fully non-linear Boussinesq equations in\udcontravariant formulation, in which Christoffel symbols are avoided, in order to\udsimulate wave transformation phenomena, wave breaking and near shore\udcurrents in computational domains representing the complex morphology of real\udcoastal regions. The motion equations retain the term related to the\udapproximation to the second order of the vertical vorticity. A new Upwind\udWeighted Essentially Non-Oscillatory scheme for the solution of the fully non-\udlinear Boussinesq equations on generalised curvilinear coordinate systems is\udproposed. The equations are rearranged in order to solve them by a high\udresolution hybrid finite volume–finite difference scheme. The conservative part\udof the above-mentioned equations, consisting of the convective terms and the\udterms related to the free surface elevation, is discretised by a high-order shock-\udcapturing finite volume scheme; dispersive terms and the term related to the\udapproximation to the second order of the vertical vorticity are discretised by a\udcell-centred finite difference scheme. The shock-capturing method makes it\udpossible to intrinsically model the wave breaking, therefore no additional terms\udare needed to take into account the breaking related energy dissipation in the surf\udzone. The model is applied on a real case regarding the simulation of wave fields\udand nearshore currents in the coastal region opposite Pescara harbour (Italy)

Contravariant Boussinesq equations for the simulation of wave transformation, breaking and run-up