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In a recent study [DutykhDias2007] we presented a novel visco-potential free surface flows formulation. The governing equations contain local and nonlocal dissipative terms. From physical point of view, local dissipation terms come from…
This study explores the use of fractional calculus as a possible tool to model wave propagation in complex, heterogeneous media. We illustrate the methodology by focusing on elastic wave propagation in a one-dimensional periodic rod. The…
We develop a high order accurate numerical method for solving the elastic wave equation in second-order form. We hybridize the computationally efficient Cartesian grid formulation of finite differences with geometrically flexible…
A generalized version of the $abcd$-Boussinesq class of systems is derived to accommodate variable bottom topography in two-dimensional space. This extension allows for the conservation of suitable energy functionals in some cases and…
In this paper, we use a straightforward numerical method to solve scattering models in one-dimensional lattices based on a tight-binding band structure. We do this by using the wave packet approach to scattering, which presents a more…
In this work we derive evolution equations for the nonlinear behavior of a coasting beam under the influence of a resonator impedance. Using a renormalization group approach we find a set of coupled nonlinear equations for the beam density…
We present a generalized (2+1)-dimensional Boussinesq equation, including two cases which are called the plus Boussinesq equation and the minus one. To investigate these equations, we apply the $\bar{\partial}$ approach to a coupled…
Considered here are two systems of equations modeling the two-way propagation of long-crested, long-wavelength internal waves along the interface of a two-layer system of fluids in the Benjamin-Ono and the Intermediate Long-Wave regime,…
The study points out that the traditional solutions to wave equation of dissipative wave and motion equation of block for a multi-degree-of-freedom mass spring damper system are the possible solutions, which are not necessarily objective…
This paper deals with the interactions of waves governed by a non-linear dispersive Boussinesq type system with the vertical displacement of a cylindrical floating structure in an axisymmetric without swirl situation. The Boussinesq regime…
In this paper we provide a formal derivation of both the Camassa-Holm equation and the fractional Camassa-Holm equation for the propagation of small-but-finite amplitude long waves in a nonlocally and nonlinearly elastic medium. We first…
This work studies the stability of solitary waves of a class of sixth-order Boussinesq equations.
Multi-scale wave propagation problems are computationally costly to solve by traditional techniques because the smallest scales must be represented over a domain determined by the largest scales of the problem. We have developed and…
We study the behavior of shallow water waves over periodically-varying bathymetry, based on the first-order hyperbolic Saint-Venant equations. Although solutions of this system are known to generally exhibit wave breaking, numerical…
Elastic wave propagation is studied in a heterogeneous 2-D medium consisting of an elastic matrix containing randomly distributed circular elastic inclusions. The aim of this study is to determine the effective wavenumbers when the incident…
A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…
The aim of this article is to study the attenuation of transient low-frequency waves in 2D lattices in both plane and antiplane problems. The main idea of this article is that analytical solutions to problems of mechanics of discrete…
We propose a Boussinesq-type model to study the surface/interfacial wave manifestation of an underlying, slowly-varying, long-wavelength, baroclinic flow in a two-layer, density-stratified system. The results of our model show numerically…
Dilatational and shear surface viscosities are highly correlated parameters, making their individual contributions difficult to disentangle in Stokes flow, linearised flow models, or two-dimensional flows. We therefore investigate the…
In this study, the numerical analysis of a specific fluid-solid interaction problem is detailed. The weakly nonlinear Boussinesq system is considered with the addition of a solid object lying on the flat bottom, allowed to move horizontally…