We introduce a new class of Green-Naghdi type models for the propagation of internal waves between two (1 + 1)-dimensional layers of homogeneous, immiscible, ideal, incompressible, irrotational fluids, vertically delimited by a flat bottom and a rigid lid. These models are tailored to improve the frequency dispersion of the original bi-layer Green-Naghdi model, and in particular to manage high-...

This note is concerned with the linear (and linearized) Type III thermoelastodynamic theory proposed by Green and Naghdi. We here assume that the mass density is positive and the thermal conductivity tensor is positive definite. However, we do not assume the positivity of any other tensor. In this situation, we obtain Hölder continuous dependence results on the supply terms. We also sketch how ...

The present paper aims to study the effect of initial stress on the 2–D problem of a homogeneous, isotropic, generalized thermo-viscoelastic material with voids in the context of Green–Naghdi theory. The modulus of elasticity is taken as a linear function of reference temperature. The analytical expressions for the physical quantities are obtained in the physical domain by using the normal mode...

A study is made of the propagation of time-harmonic plane thermoelastic waves of assigned frequency in an infinite rotating medium using Green-Naghdi model (1993) of linear thermoelasticity without energy dissipation. A more general dispersion equation is derived to examine the effect of rotation on the phase velocity of the modified coupled thermal dilatational shear waves. It is observed that...

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 paper, we consider a one-dimensional fully nonlinear weakly dispersive Green-Naghdi model for shallow water waves over variable bottom topographies. Such model describes a large spectrum of shallow water waves, and it is thus of great importance to design accurate and robust numerical methods for solving it. The governing equations contain mixed spatial and temporal derivatives of the u...

This work is devoted to the structure of time-discrete Green--Naghdi equations including bathymetry. We use projection characterize homogeneous and inhomogeneous boundary conditions for which semidiscrete are well posed. allows us propose efficient robust numerical treatment that ensures entropy stability scheme by construction. Numerical evidence provided illustrate our approach suitable situa...

SM1. Introduction. This supplement contains details that were omitted from the main paper [SM2] because of page limitations. SM2. The Model for the Shell Structure Acoustic Interaction. To avoid switching between the main paper and this supplement, we have included the entire expanded version of Section 2, not only the details and proofs missing from Section 2 of the main paper. SM2.1. Naghdi S...