Dispersive shallow water wave modelling. Part II: Numerical simulation on a globally flat space

TL;DR

This paper presents an adaptive finite volume numerical scheme for the weakly dispersive Serre-Green-Naghdi model, utilizing moving grids and solving elliptic equations for non-hydrostatic pressure to improve simulation accuracy.

Contribution

It introduces a novel adaptive numerical method with moving grids for the SGN model, enhancing the simulation of dispersive shallow water waves.

Findings

Effective simulation of dispersive shallow water waves

Use of moving grids improves accuracy and efficiency

Well-posed boundary conditions for the model

Abstract

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 effective 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 nonlinear elliptic equation. Moreover, this form of governing equations allows determining the natural form of boundary conditions to obtain a well-posed (numerical) problem.