An application of the finite element method for solving the system of partial differential equations
An application of the finite element method for solving the system of partial differential equations
An entropy satisfying scheme for two-layer shallow water equations with uncoupled treatment
We consider the system of partial differential equations governing the one-dimensional flow of two superposed immiscible layers of shallow water. The difficulty in this system comes from the coupling terms involving some derivatives of the unknowns that make the system nonconservative, and eventually nonhyperbolic. Due to these terms, a numerical scheme obtained by performing an arbitrary scheme to each layer, and using time-splitting or other similar techniques leads to instabilities in...
An entropy-correction free solver for non-homogeneous shallow water equations
In this work we introduce an accurate solver for the Shallow Water Equations with source terms. This scheme does not need any kind of entropy correction to avoid instabilities near critical points. The scheme also solves the non-homogeneous case, in such a way that all equilibria are computed at least with second order accuracy. We perform several tests for relevant flows showing the performance of our scheme.
An entropy-correction free solver for non-homogeneous shallow water equations
In this work we introduce an accurate solver for the Shallow Water Equations with source terms. This scheme does not need any kind of entropy correction to avoid instabilities near critical points. The scheme also solves the non-homogeneous case, in such a way that all equilibria are computed at least with second order accuracy. We perform several tests for relevant flows showing the performance of our scheme.
An existence result for a free boundary shallow water model using a lagrangian scheme
Analysis of Thacker's method for solving the linearized shallow water equations
Analytical and numerical solutions to initial-boundary value problems of the water wave motion in a reservoir.
Approximate solution for Euler equations of stratified water via numerical solution of coupled KdV system.
Approximate traveling wave solutions of coupled Whitham-Broer-Kaup shallow water equations by homotopy analysis method.
Asymptotic analysis of surface waves due to high-frequency disturbances
The present paper is devoted to the asymptotic analysis of the linear unsteady surface waves. We study two problems concerned with high-frequency surface and submerged disturbances. The two-scale asymptotic series are obtained for the velocity potential. The principal terms in the asymptotics of some hydrodynamical characteristics of the wave motion (the free surface elevation, the energy, etc.) are described.
Asymptotic behavior of solutions of the damped Boussinesq equation in two space dimensions.
Asymptotic behaviors of internal waves
We present here a systematic method of derivation of asymptotic models for internal waves, that is, for the propagation of waves at the interface of two fluids of different densities. Many physical regimes are investigated, depending on the physical parameters (depth of the fluids, amplitude and wavelength of the interface deformations). This systematic method allows us to recover the many models existing in the literature and to derive some new models, in particular in the case of large amplitude...
Asymptotic behaviour in planar vortex theory
The asymptotic behaviour of solutions of a class of free-boundary problems arising in vortex theory is discussed.
Asymptotic behaviour of solutions to the Korteweg-deVries-Burgers system
Asymptotic stability of a stationary flowing regime of an ideal incompressible fluid.
Asymptotic study of the vibration problem for an elastic body deeply immersed in an incompressible fluid
Attractor for a viscous coupled Camassa-Holm equation.
Basic singularities in the theory of internal waves with surface tension.
Benjamin–Ono periodic bifurcating water waves in presence of an essential spectrum