Dispersive Shallow Water Wave Modelling. Part II: Numerical Simulation on a Globally Flat Space

摘要

In this paper, we describe a numerical method to solve numerically the weaklydispersive fully nonlinear Serre-Green-Naghdi (SGN) celebrated model. Namely,our scheme is based on reliable finite volume methods, proven to be veryeffective for the hyperbolic part of equations. The particularity of our studyis that we develop an adaptive numerical model using moving grids. Moreover, weuse a special form of the SGN equations where non-hydrostatic part of pressureis found by solving a nonlinear elliptic equation. Moreover, this form ofgoverning equations allows determining the natural form of boundary conditionsto obtain a well-posed (numerical) problem.