Application Of Boussinesq Model And Non-hydrostatic Model In The Hydrodynamic Calculation At Reefs

The hydrodynamic at reefs is the research hotspots and has the character of large variation of depth and rapidly variable topography.The research faces many difficulties,including violent wave breaking,strong nonlinearity,complexity and variability of flow state,complex components of wave and coexistence of long/short wave.In this paper,Boussinesq numerical model and the non-hydrostatic model based on Euler equation are used in the simulation of wave transformation at reefs.With a shock-capturing numerical model based on second-order fully nonlinear Boussinesq equations,this paper describes the simulation of propagation and deformation of regular wave and irregular wave over reef flats.A hybrid high-order finite-volume and finitedifference method is used to solve conservative governing equations.Wave breaking is treated as shock waves and the hydrostatic construction technique is used for wet-dry fronts.In this paper,research on wave height spatial distribution,mean water level changes over reef flat and wave energy spectrum shifts was presented.The numerical results are in close agreement with the physical model experimental results,showing that the numerical model used in this paper has good stability,excellent shock-capturing ability and can treat wet-dry moving boundary.Therefore,this model can well simulate hydrodynamics performance in the process of wave propagation over reef flats.Based on the study above,researching the effect on wave transformation caused by varied reef-front slope and depth at reef flats.The non-hydrostatic model in this paper is still in development.The governing equations are Euler equations,using a ? coordinate.Based on rectangular grid,a combined finitevolume and finite-difference scheme with a Godunov-type method is applied to discretize equations.In order to apply the pressure boundary condition,the velocities are defined at cell center while the pressure is placed at cell faces.The MUSTA scheme is used to estimate fluxes at cell faces,and the time-integration scheme is first-order explicit Euler.Through the fractional step procedure,the governing equations are divided into predictor step and corrector step.The shock-capturing numerical scheme introduced into the non-hydrostatic model is capable of capturing wave breaking without any criterion and empirical energy-loss formulation for wave breaking.Partial performance of this model is validated using several tests,and then this model are used in simulation of wave propagation over reefs.The simulated significant wave height and mean water level shows no accordance with experimental data,meaning that there is a big shortage in this non-hydrostatic model and the further development is necessary.