Research Of Numerical Simulation Method Of Multidirectional Wave Breaking And Incident Waves Based On FEM Model Of Boussinesq Equations

Research on wave propagation and spatial-temporal distribution is vitally impotant for offshore production operations and engineering design.Actually,the nearshore topography is complex with spatially inhomogeneous multidirectional irregular waves,and the propagation wave is usually accompanied by breaking due to the shallow water depth.Therefore,to establish a numerical calculation model,which can effectively simulate nearshore wave breaking and consider spatially inhomogeneous wave incidence has great significance to study wave characteristics and wave action on buildings.Boussinesq equations,is a preferable mathematical model to describe nearshore wave propagation.While,based on the assumption of potential flow,the model cannot directly simulate turbulent motion and wave dissipation due to wave breaking during wave propagation.In the paper,to establish a more effective numerical calculation model,the dissipative terms are introduced in the momentum equation of the improved Boussinesq equations derived by Beji and Nadaoka to model wave breaking and friction.Further,a numerical model based on an unstructured finite element method(FEM)with linear triangle element is established.Considering that the real sea waves are obliquely incident or multidirectional irregular waves,the established numerical model is firstly applied to simulate wave propagation on a relatively steep slope topography of 1:5.Various kinds of waves including normal and oblique incident regular and irregular,waves,multidirectional irregular waves are considered.The numerical results are compared with the corresponding physical results.Satisfactory agreements between the numerical and experimental results including the distribution of wave height,wave spectra as well as directional distribution,etc,verifies that the established model is effective for the simulation of wave propagation and breaking about obliquely incident and multidirectional irregular waves on a relative steep slope.Numerical simulation results also indicates that the initial breaking threshold parameter ?t(I)is the main factor affecting simulation accuracy of wave breaking.The optimum parameter should consider different values for normally and obliquely incident waves as well as multidirectional irregular waves,they are?t(I)=0.55(?)??t(I)=0.65(?)and ?t(I)=0.75(?),respectively.Besides,with the deeper study of nearshore issues and the improvement of the experimental technology requirements,not only the simulation of real wave propagation in given region should meet the requirements of statistical properties,also,the simulated waves should be consistent with the given/real wave elevation histories,that is,deterministic simulation of waves.According to the given/real wave time series in known area and based on a single summation model,two deterministic wave reconstruction methods of EEED and PTPD approaches are proposed.Theoretically and numerically simulated multidirectional irregular waves with different directional distribution width and wave steepness Hs/Ls based on the established numerical model are reconstructed(in which,Hs and Ls represent significant wave height and wavelength respectively).Further,the two proposed methods are extended to calculate wave incident boundary conditions of the numerical model on the basis of the time serise in given region.Thus,the deterministic simulation of multidirectional irregular waves in a numerical tank is realized,that is,the given wave time series are reproduced in a specific region.The consistency between the reconstructed and the given/real wave elevation histories proves that the EEED and PTPD methods are acceptable.Wave reconstruction error Er between the reconstructed and the given/real time series increase with the scope size rr/Ls increasing and the range of the directional distribution width is the dominant factor affecting the reconstruction accuracy.The PTPD approach is generally better than EEED method as the optimum relative separations of the wave gauges R for PTPD approach to be kept smaller than 0.12Ls,instead,the EEED approach is advised when R is large.Meanwhile,considering the spatial inhomogeneity of the wave at incident boundary that used to numerically calculate nearshore wave propagation,the inhomogeneous incident wave boundary simulation Inhomog-Bound-EEED and Inhomog-Bound-PTPD approaches are firstly proposed using a single summation model based on the deterministic wave reconstruction EEED and PTPD methods and the given/real wave time series in certain spatial wave incident boundary.The incident boundary waves of the Boussinesq model is simulated using the established methods according to the time series of the inhomogeneity wave field in diffraction region calculated by the theoretical diffraction model.The agreement between the numerical and theoretically simulated results verifies that the effectiveness of the two proposed incident wave boundary simulation methods.Further,for the inhomogeneious wave field that cannot synchronously get the real wave elevation histories,the non-uniform distributed directional spectra information with certain spatial is considered.A directional-spectrum-single-frequencyper-direction inhomogeneous wave incident boundary simulation method,i.e.,InhomogBound-DSFD method based on a double summation model is proposed.Similarly,the incident wave boundary of the Boussinesq model is simulated using Inhomog-Bound-DSFD method.Then,the Boussinesq model is coupled with the theoretical diffraction model and SWAN model by the provided directional spectra along the boundary.The effectiveness of the InhomogBound-DSFD approach is preferably tested by the consistent of the directional distributions and significant wave heights of the numerical wave field with the corresponding results of the theoretical diffraction model and the SWAN model.In the paper,the established numerical calculation model can be used to simulate offshore wave breaking of multidirectional irregular waves,can deterministically simulate waves in the numerical wave thank and consider the spatial inhomogeneity of the wave on the incident boundary.These can provide technology support for effective simulation of wave propagation.