A method for solving a boundary value problem for a partial differential equation of elliptic type.
A -scheme for a class of systems of coupled conservation laws with source term. Application to a two-layer 1-D shadow water system
The goal of this paper is to construct a first-order upwind scheme for solving the system of partial differential equations governing the one-dimensional flow of two superposed immiscible layers of shallow water fluids. This is done by generalizing a numerical scheme presented by Bermúdez and Vázquez-Cendón [3, 26, 27] for solving one-layer shallow water equations, consisting in a -scheme with a suitable treatment of the source terms. The difficulty in the two layer system comes from the coupling...
A Q-scheme for a class of systems of coupled conservation laws with source term. Application to a two-layer 1-D shallow water system
The goal of this paper is to construct a first-order upwind scheme for solving the system of partial differential equations governing the one-dimensional flow of two superposed immiscible layers of shallow water fluids. This is done by generalizing a numerical scheme presented by Bermúdez and Vázquez-Cendón [3, 6, 27] for solving one-layer shallow water equations, consisting in a Q-scheme with a suitable treatment of the source terms. The difficulty in the two layer system comes from the coupling...
Approximate solution for Euler equations of stratified water via numerical solution of coupled KdV system.
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...