The fully nonlinear and weakly dispersive Green-Naghdi equations for shallow water waves of large amplitude is studied. An hybrid finite volume and finite difference splitting approach is proposed. Numerical validations are then performed in one horizontal dimension.

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...

We give a brief survey of applications of the Gearhart-Prüss spectral mapping theorem for abstract strongly continuous semigroups on Hilbert spaces to the study of stability of solitary waves for a large class of Hamiltonian partial differential equations of mathematical physics including Klein-Gordon, nonlinear Schrödinger, Boussinesq, Benjamin-BonaMahoney (regularized long-wave), Korteweg-deV...

A new nonlinear equation governing asymptotic dynamics of ripples is derived by using a short wave perturbative expansion on a generalized version of the Green-Naghdi system. It admits peakon solutions with amplitude, velocity and width in interrelation and static compacton solutions with amplitude and width in interrelation. Short wave pattern formation is shown to result from a balance betwee...

We study the linear theory of thermo-electro-viscoelasticity Green–Naghdi type for case a one-dimensional body. For corresponding mathematical model, we prove uniqueness theorem solution to mixed boundary-initial-value problem by means Laplace transform after rewriting constitutive equations in an appropriate form. Moreover, derive result continuous dependence upon supply terms.

The objective stress rates used in most commercial finite element programs are the Jaumann rate of Kirchhoff stress, Jaumann rates of Cauchy stress, or Green–Naghdi rate. The last two were long ago shown not to be associated by work with any finite strain tensor, and the first has often been combined with tangential moduli not associated by work. The error in energy conservation was thought to ...