Related papers: A multiscale model for weakly nonlinear shallow wa…
This paper is concerned with the derivation of a two-component system modelling shallow-water waves with constant vorticity under the Camassa-Holm scaling from our newly established Green-Naghdi equations with a linear shear. It is worth…
Wave propagation in complex media is a universal problem spanning optics, acoustics, mechanics, and condensed matter physics. While disorder usually causes strong scattering, recent theory predicts that a special class of correlated…
We present a new stabilised and efficient high-order nodal spectral element method based on the Mixed Eulerian Lagrangian (MEL) method for general-purpose simulation of fully nonlinear water waves and wave-body interactions. In this MEL…
We study hyperbolic systems of one-dimensional partial differential equations under general, possibly non-local boundary conditions. A large class of evolution equations, either on individual 1-dimensional intervals or on general networks,…
In the first part of this article we present some exact solutions for special hyperbolic-parabolic systems with sustained oscillations induced by the initial data, most notably the compressible Navier-Stokes system with non-monotone…
We propose a generalized finite element method for the strongly damped wave equation with highly varying coefficients. The proposed method is based on the localized orthogonal decomposition introduced and is designed to handle independent…
In this paper we consider the Benjamin equation, a partial differential equation that models one-way propagation of long internal waves of small amplitude along the interface of two fluid layers under the effects of gravity and surface…
In this study we investigate shallow turbidity density currents and underflows from mechanical point of view. We propose a simple hyperbolic model for such flows. On one hand, our model is based on very basic conservation principles. On the…
We prove global well-posedness of the initial value problem for a class of variational quasilinear wave equations, in one spatial dimension, with initial data that is not-necessarily small. Key to our argument is a form of quasilinear null…
A numerical method is proposed for solving the two layer shallow water equations with variable bathymetry in one dimension based on high-resolution f-wave-propagation finite volume methods. The method splits the jump in the fluxes and…
A wave front and a wave back that spontaneously connect two hyperbolic equilibria, known as a heteroclinic wave loop, give rise to periodic waves with arbitrarily large spatial periods through the heteroclinic bifurcation. The nonlinear…
We investigate the perturbations induced by a periodic bathymetry on traveling Boussinesq solitons in a two-dimensional configuration. We present two perturbation approaches to solve the nonlinear, dispersive and non-autonomous differential…
We study the Vlasov-Poisson-Fokker-Planck system with uncertainty and multiple scales. Here the uncertainty, modeled by random variables, enters the solution through initial data, while the multiple scales lead the system to its high-field…
We present a new high-order accurate computational fluid dynamics model based on the incompressible Navier-Stokes equations with a free surface for the accurate simulation of nonlinear and dispersive water waves in the time domain. The…
We present a discontinuous finite element method for the shallow water equations which exploits high-resolution realistic bathymetry data without any regularity assumption, also in the case of high-order discretizations. We prove a number…
This paper aims to give a refined wave breaking description of the Cauchy problem to the one-dimensional nonlinear shallow water equations providing a sharp estimate of the lifespan of the solutions depending on the amplitude and topography…
We derive and analyse well-posed boundary conditions for the linear shallow water wave equation. The analysis is based on the energy method and it identifies the number, location and form of the boundary conditions so that the initial…
We apply a multiple-time version of the reductive perturbation method to study long waves as governed by the shallow water wave model equation. As a consequence of the requirement of a secularity-free perturbation theory, we show that the…
We study wave turbulence in shallow water flows in numerical simulations using two different approximations: the shallow water model, and the Boussinesq model with weak dispersion. The equations for both models were solved using periodic…
This work develops a dynamic homogenization approach for metamaterials. It finds an approximate macroscopic homogenized equation with constant coefficients posed in space and time; however, the resulting homogenized equation is higher order…