Nearly concentric Korteweg-de Vries equation and periodic traveling wave solution.
Nested axi-symmetric vortex rings
New solitons and periodic solutions for Thekadomtsev-Petviashvili equation.
Non existence of standing waves for hyperbolic Davey-Stewartson systems
Nonexistence of simple hyperbolic blow-up for the quasi-geostrophic equation.
Nonlinear diffraction of water waves by offshore structures.
Nonlinear instability in an ideal fluid
Nonlinear Scattering for Some Dispersive Equations Generalizing Benjamin-Bona-Mahony Equation.
Nonlinear stationary surface waves above an underwater ridge.
Note on modulational instability of Boussinesq wavetrains.
Numerical Analysis of Cavitational Flow-Theory.
Numerical approximation of the inviscid 3D primitive equations in a limited domain
A new set of nonlocal boundary conditions is proposed for the higher modes of the 3D inviscid primitive equations. Numerical schemes using the splitting-up method are proposed for these modes. Numerical simulations of the full nonlinear primitive equations are performed on a nested set of domains, and the results are discussed.
Numerical approximation of the inviscid 3D primitive equations in a limited domain
A new set of nonlocal boundary conditions is proposed for the higher modes of the 3D inviscid primitive equations. Numerical schemes using the splitting-up method are proposed for these modes. Numerical simulations of the full nonlinear primitive equations are performed on a nested set of domains, and the results are discussed.
Numerical comparisons of two long-wave limit models
The Benney-Luke equation (BL) is a model for the evolution of three-dimensional weakly nonlinear, long water waves of small amplitude. In this paper we propose a nearly conservative scheme for the numerical resolution of (BL). Moreover, it is known (Paumond, Differential Integral Equations 16 (2003) 1039–1064; Pego and Quintero, Physica D 132 (1999) 476–496) that (BL) is linked to the Kadomtsev-Petviashvili equation for almost one-dimensional waves propagating in one direction. We study here numerically...
Numerical comparisons of two long-wave limit models
The Benney-Luke equation (BL) is a model for the evolution of three-dimensional weakly nonlinear, long water waves of small amplitude. In this paper we propose a nearly conservative scheme for the numerical resolution of (BL). Moreover, it is known (Paumond, Differential Integral Equations16 (2003) 1039–1064; Pego and Quintero, Physica D132 (1999) 476–496) that (BL) is linked to the Kadomtsev-Petviashvili equation for almost one-dimensional waves propagating in one direction. We study here numerically...
Numerical computations for solidification problems with change of volume
Numerical evidence of nonuniqueness in the evolution of vortex sheets
We consider a special configuration of vorticity that consists of a pair of externally tangent circular vortex sheets, each having a circularly symmetric core of bounded vorticity concentric to the sheet, and each core precisely balancing the vorticity mass of the sheet. This configuration is a stationary weak solution of the 2D incompressible Euler equations. We propose to perform numerical experiments to verify that certain approximations of this flow configuration converge to a non-stationary...
Numerical simulation of the field velocities and local disturbances of a long gravity wave passing above an immersed vertical barrier.
Numerical simulations of wave breaking
This paper is devoted to the numerical simulation of wave breaking. It presents the results of a numerical workshop that was held during the conference LOMA04. The objective is to compare several mathematical models (compressible or incompressible) and associated numerical methods to compute the flow field during a wave breaking over a reef. The methods will also be compared with experiments.
Numerical simulations of wave breaking
This paper is devoted to the numerical simulation of wave breaking. It presents the results of a numerical workshop that was held during the conference LOMA04. The objective is to compare several mathematical models (compressible or incompressible) and associated numerical methods to compute the flow field during a wave breaking over a reef. The methods will also be compared with experiments.