In this paper, we introduce artificial boundary conditions for the linearized Green-Naghdi system of equations. The derivation of such continuous (respectively discrete) boundary conditions include the inversion of Laplace transform (respectively Z-transform) and these boundary conditions are in turn non local in time. In the case of continuous boundary conditions, the inversion is done explici...

Head-on collision of two solitary waves in the presence linear shear currents is studied by use High-Level Green–Naghdi (HLGN) theory. The finite difference method used to solve HLGN model time-domain simulation. initial values are obtained steady solution currents. Shear with different velocities considered assess their effect on solitary-wave collision. Three aspects head-on process current s...

Abstract This paper is on arbitrary high order fully discrete one-step ADER discontinuous Galerkin schemes with subcell finite volume limiters applied to a new class of first hyperbolic reformulations nonlinear dispersive systems based an extended Lagrangian approach introduced by Dhaouadi et al. (Stud Appl Math 207:1–20, 2018), Favrie and Gavrilyuk (Nonlinearity 30:2718–2736, 2017). We conside...

a series of schiff bases of ni(ii) and cu(ii) using acetylacetone (acac), salicylaldehyde (sal), ethylenediamine (en), and o-phenylendiarnine (dabe) were prepared and characterized. the electronic spectra of some copper chelates in various organic solvents depend strongly on the solvent used and the d-d band of cu(ii) shifts to red with the increase of the donor number (dn) of solvent. the colo...

We consider strongly-nonlinear and weakly-dispersive surface water waves governed by equations of Boussinesq type, known as the Serre–Green–Naghdi system; it describes future states free depth averaged horizontal velocity, given their initial state. The lack knowledge velocity field well provided measurements lead to an ill-posed problem that cannot be solved traditional techniques. To this end...

Abstract In some configurations, dispersion effects must be taken into account to improve the simulation of complex fluid flows. A family free-surface dispersive models has been derived in Fernández-Nieto et al. (Commun Math Sci 16(05):1169–1202, 2018). The hierarchy is based on a Galerkin approach and parameterised by number discrete layers along vertical axis. this paper we propose numerical ...