Dispersive Shallow Water Wave Modelling. Part II: Numerical Simulation on a Globally Flat Space (Communications in Computational Physics, 2018)
In this paper we describe a numerical method to solve numerically theweakly dispersive fully nonlinear SERRE–GREEN–NAGHDI (SGN) celebrated model.Namely, our scheme is based on reliable finite volume methods, proven to be very efficientfor the hyperbolic part of equations. The particularity of our study is that wedevelop an adaptive numerical model using moving grids. Moreover, we use a specialform of the SGN equations where non-hydrostatic part of pressure is found by solvinga linear elliptic equation. Moreover, this form of governing equations allows todetermine the natural form of boundary conditions to obtain a well-posed (numerical)problem.
Keywords: Nonlinear dispersive waves; non-hydrostatic pressure; moving adaptive grids; finite volumes; conservative finite differences.