Numerical simulation of wave transformation,breaking and runup by a contravariant fully non-linear Boussinesq equations model  

作　　者：F.GALLERANO G.CANNATA F.LASAPONARA 

机构地区：[1]Department of Civil, Constructional and Environmental Engineering, Sapienza University of Rome

出　　处：《Journal of Hydrodynamics》2016年第3期379-388,共10页水动力学研究与进展B辑（英文版）

摘　　要：In this paper we propose a new model based on a contravariant integral form of the fully non-linear Boussinesq equations （FNBE） in order to simulate wave transformation phenomena, wave breaking, runup and nearshore currents in computational domains representing the complex morphology of real coastal regions. The above-mentioned contravariant integral form, in which Christoffel symbols are absent, is characterized by the fact that the continuity equation does not include any dispersive term. The Boussinesq equation system is numerically solved by a hybrid finite volume-f＇mite difference scheme. A high-order upwind weighted essentially non-oscillatory （WENO） finite volume scheme that involves an exact Riemann solver is implemented. The wave breaking is represented by discontinuities of the weak solution of the integral form of the non-linear shallow water equations （NSWE）. On the basis of the shock-capturing high order WENO scheme a new procedure, for the computation of the structure of the solution of a Riemann problem associated with a wet/dry front, is proposed in order to simulate the run up hydrodynamics in swash zone. The capacity of the proposed model to correctly represent wave propagation, wave breaking, run up and wave induced currents is verified against test cases present in literature. The results obtained are compared with experimental measures, analytical solutions or alternative numerical solutions. The proposed model is applied to a real case regarding the simulation of wave fields and nearshore currents in the coastal region opposite San Mauro Cilento （Italy）.In this paper we propose a new model based on a contravariant integral form of the fully non-linear Boussinesq equations （FNBE） in order to simulate wave transformation phenomena, wave breaking, runup and nearshore currents in computational domains representing the complex morphology of real coastal regions. The above-mentioned contravariant integral form, in which Christoffel symbols are absent, is characterized by the fact that the continuity equation does not include any dispersive term. The Boussinesq equation system is numerically solved by a hybrid finite volume-f＇mite difference scheme. A high-order upwind weighted essentially non-oscillatory （WENO） finite volume scheme that involves an exact Riemann solver is implemented. The wave breaking is represented by discontinuities of the weak solution of the integral form of the non-linear shallow water equations （NSWE）. On the basis of the shock-capturing high order WENO scheme a new procedure, for the computation of the structure of the solution of a Riemann problem associated with a wet/dry front, is proposed in order to simulate the run up hydrodynamics in swash zone. The capacity of the proposed model to correctly represent wave propagation, wave breaking, run up and wave induced currents is verified against test cases present in literature. The results obtained are compared with experimental measures, analytical solutions or alternative numerical solutions. The proposed model is applied to a real case regarding the simulation of wave fields and nearshore currents in the coastal region opposite San Mauro Cilento （Italy）.

关 键 词：fully non-linear Boussinesq equations contravariant formulation Christoffel symbols upwind WENO scheme wet-dryfronts 

分 类 号：O241.8[理学—计算数学]