A mathematical model for core-annular fluids with surfactants.
A note on the solution of the von Kármán equations using series and Chebyshev spectral methods.
A study of bifurcation of Kolmogorov flows with an emphasis on the singular limit.
An application of the method of matched asymptotic expansions for low Reynolds number flow past a cylinder of arbitrary cross-section.
An approximate solution for flow between two disks rotating about distinct axes at different speeds.
Approximate ad hoc parametric solutions for nonlinear first-order PDEs governing two-dimensional steady vector fields.
Asymptotic analysis of the structure of a steady planar detonation: Review and extension.
Asymptotic and numerical modelling of flows in fractured porous media
This study concerns some asymptotic models used to compute the flow outside and inside fractures in a bidimensional porous medium. The flow is governed by the Darcy law both in the fractures and in the porous matrix with large discontinuities in the permeability tensor. These fractures are supposed to have a small thickness with respect to the macroscopic length scale, so that we can asymptotically reduce them to immersed polygonal fault interfaces and the model finally consists in a coupling between...
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...
Derivation and well-posedness of Boussinesq/Boussinesq systems for internal waves
We consider the propagation of internal waves at the interface between two layers of immiscrible fluids of different densities, under the rigid lid assumption, with the presence of surface tension and with uneven bottoms. We are interested in the case where the flow has a Boussinesq structure in both the upper and lower fluid domains. Following the global strategy introduced recently by Bona, Lannes and Saut [J. Math. Pures Appl. 89 (2008)], we derive an asymptotic model in this regime, namely the...
Effects of Poiseuille flow on peristaltic transport.
Hydrodynamic effect on the three-dimensional flow past a vertical porous plate.
Hydrodynamic flow between rotating eccentric cylinders with suction at the porous walls.
Incompressible, inviscid limit of the compressible Navier–Stokes system
Induced dusty flow due to normal oscillation of wavy wall.
Influence of bottom topography on long water waves
We focus here on the water waves problem for uneven bottoms in the long-wave regime, on an unbounded two or three-dimensional domain. In order to derive asymptotic models for this problem, we consider two different regimes of bottom topography, one for small variations in amplitude, and one for strong variations. Starting from the Zakharov formulation of this problem, we rigorously compute the asymptotic expansion of the involved Dirichlet-Neumann operator. Then, following the global strategy...
Interaction of shock waves in gas dynamics: uniform in time asymptotics.
Local smooth solution and non-relativistic limit of radiation hydrodynamics equations.
Low-Mach consistency of a class of linearly implicit schemes for the compressible Euler equations
In this note, we give an overview of the authors’ paper [6] which deals with asymptotic consistency of a class of linearly implicit schemes for the compressible Euler equations. This class is based on a linearization of the nonlinear fluxes at a reference state and includes the scheme of Feistauer and Kučera [3] as well as the class of RS-IMEX schemes [8,5,1] as special cases. We prove that the linearization gives an asymptotically consistent solution in the low-Mach limit under the assumption of...
Modeling of coupled roll and yaw damping of a floating body in waves.