In this paper we describe a numerical method to solve numerically the weakly dispersive fully nonlinear SERRE-GREEN-NAGHDI(SGN)celebrated model.Namely,our scheme is based on reliable finite volume methods,proven to be...In this paper we describe a numerical method to solve numerically the weakly dispersive fully nonlinear SERRE-GREEN-NAGHDI(SGN)celebrated model.Namely,our scheme is based on reliable finite volume methods,proven to be very efficient for the hyperbolic part of equations.The particularity of our study is that we develop an adaptive numerical model using moving grids.Moreover,we use a special form of the SGN equations where non-hydrostatic part of pressure is found by solving a linear elliptic equation.Moreover,this form of governing equations allows to determine the natural form of boundary conditions to obtain a well-posed(numerical)problem.展开更多
基金This research was supported by RSCF project No 14-17-00219.The authors would like to thank Prof.Emmanuel AUDUSSE(UniversitéParis 13,France)who brought our attention to the problem of boundary conditions for the SGN equations.
文摘In this paper we describe a numerical method to solve numerically the weakly dispersive fully nonlinear SERRE-GREEN-NAGHDI(SGN)celebrated model.Namely,our scheme is based on reliable finite volume methods,proven to be very efficient for the hyperbolic part of equations.The particularity of our study is that we develop an adaptive numerical model using moving grids.Moreover,we use a special form of the SGN equations where non-hydrostatic part of pressure is found by solving a linear elliptic equation.Moreover,this form of governing equations allows to determine the natural form of boundary conditions to obtain a well-posed(numerical)problem.
