Abstract
We study the Serre-Green-Naghdi system under a non-hydrostatic formulation, modelling incompressible free surface flows in shallow water regimes. This system, unlike the well-known (nonlinear) Saint-Venant equations, takes into account the effects of the non-hydrostatic pressure term as well as dispersive phenomena. Two numerical schemes are designed, based on a finite volume - finite difference type splitting scheme and iterative correction algorithms. The methods are compared by means of simulations concerning the propagation of solitary wave solutions. The model is also assessed with experimental data concerning the Favre secondary wave experiments [12].
Highlights
The simulation of incompressible, homogeneous, inviscid free surface fluid flows as a tool to describe and examine the propagation of surface water waves has been a major field of research oriented towards oceanographic applications for the past several decades
As for the resolution of the system arising from the non-hydrostatic correction step – which is the core of this work – we present two iterative algorithms: the Uzawa algorithm applied to the mixed velocity-pressure problem and the Gauss-Seidel method for the projection elliptic step
The non-hydrostatic formulation of the well-known Serre–Green-Naghdi equations is investigated in this paper
Summary
The simulation of incompressible, homogeneous, inviscid free surface fluid flows as a tool to describe and examine the propagation of surface water waves has been a major field of research oriented towards oceanographic applications for the past several decades. Diverse models based on the (nonlinear) shallow water [or Saint Venant] system [14] have been proposed and analysed in the past (see for instance [4, 5, 8, 11, 23, 24, 26]) This model provides a reasonable tool for capturing the nonlinear transformation of waves, it fails to represent dispersive effects because of the underlying hydrostatic assumption. Simulations concerning the propagation of exact solitary waves over a flat bottom topography are run in order to compare the two algorithms, mainly in terms of computational time It is followed by simulations of a dispersive dam-break problem. The numerical validation against the experimental data obtained from the Favre secondary wave experiment [12] is presented and compared with previous results [9]
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