The Serre–Green–Naghdi (SGN) equations, also known as the fully-nonlinear Boussinesq wave equations, accurately describe the behaviour of dispersive shoaling water waves. This article presents and validates a novel combination of methods for the numerical approximation of solutions to the SGN equations. The approach preserves the robustness of the original finite-volume Saint-Venant solver, in ...

This study deals with asymptotic models for the propagation of one-dimensional internal waves at the interface between two layers of immiscible fluids of different densities, under the rigid lid assumption and with a flat bottom. We present a new Green-Naghdi type model in the Camassa-Holm (or medium amplitude) regime. This model is fully justified, in the sense that it is consistent, well-pose...

The fully nonlinear and weakly dispersive Green–Naghdi model for shallow water waves of large amplitude is studied. The original model is first recast under a new formulation more suitable for numerical resolution. An hybrid finite volume and finite difference splitting approach is then proposed, which could be adapted to many physical models that are dispersive corrections of hyperbolic system...

We derive an asymptotic formula for the amplitude distribution in a fully nonlinear shallow-water solitary wave train which is formed as the long-time outcome of the initial-value problem for the Su-Gardner (or one-dimensional Green-Naghdi) system. Our analysis is based on the properties of the characteristics of the associated Whitham modulation system which describes an intermediate “undular ...

The drift motion of a freely floating deformable ice sheet in shallow water subjected to incident nonlinear waves and uniform current is studied by use the Green–Naghdi theory for fluid thin plate an elastic sheet. wave- current-induced forces are obtained integrating hydrodynamic pressure around body. oscillations translational then determined substituting flow-induced into equation resulting ...

We shall briefly present here the main idea of partial selective reduced integration as developed in [1], [2]. As we shall see the idea is quite general and can be applied to a number of different situations. For the sake of simplicity, however, we shall concentrate on the particular case of Naghdi shell models. Once the idea is understood, its generalisation to other cases should be straightfo...

In this work we prove that the solution of Serre-Green-Naghdi equation cannot be globally defined when interface reaches impervious bottom tangentially. As a consequence, our result complements paper Camassa, R., Falqui, G., Ortenzi, Pedroni, M., & Thomson, C. Hydrodynamic models and confinement effects by horizontal boundaries. Journal Nonlinear Science, 29(4), 1445-1498, 2019. Furthermore, al...

Abstract In this investigation, a computational analysis is conducted to study magneto-thermoelastic problem for an isotropic perfectly conducting half-space medium. The medium subjected periodic heat flow in the presence of continuous longitude magnetic field. Based on Moore–Gibson–Thompson equation, new generalized model has been investigated address considered problem. introduced can be form...

the present paper is concerned with  the investigation of disturbances in a homogeneous  transversely isotropic thermoelastic rotating  medium with two temperatures, in the presence of the combined effects of   hall currents and magnetic field due to thermomechanical sources. the formulation is applied to the thermoelasticity theories developed by green-naghdi theories of type-ii and type-iii. ...