Mejdi Azaïez

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We present in this paper a numerical scheme for incompressible Navier-Stokes equations with open and traction boundary conditions, in the framework of pressure-correction methods. A new way to enforce this type of boundary condition is proposed and provides higher pressure and velocity convergence rates in space and time than found in the present state of(More)
A mixed spectral method is proposed and analyzed for the Stokes problem in a semi-infinite channel. The method is based on a generalized Galerkin approximation with Laguerre functions in the x direction and Legendre polynomials in the y direction. The well-posedness of this method is established by deriving a lower bound on the inf-sup constant. Numerical(More)
In 1999, Jean-Paul Caltagirone and Jérôme Breil have developed in their paper [Caltagirone, J. Breil, Sur une méthode de projection vectorielle pour la résolution des équations de Navier–Stokes, C.R. Acad. Sci. Paris 327(Série II b) (1999) 1179–1184] a new method to compute a divergence-free velocity. They have used the grad(div) operator to extract the(More)
We consider the flow of a viscous incompressible fluid in a rigid homogeneous porous medium provided with boundary conditions on the pressure around a circular well. When the boundary pressure presents high variations, the permeability of the medium depends on the pressure, so that the model is nonlinear. We propose a spectral discretization of the(More)
We consider the Navier–Stokes equations in a twoou three-dimensional domain provided with non standard boundary conditions which involve the normal component of the velocity and the tangential components of the vorticity. We write a variational formulation of this problem with three independent unknowns: the vorticity, the velocity and the pressure, and(More)
We show how Lagrangian coordinates provide an effective representation of how difficult non-linear, hyperbolic transport problems in porous media can be dealt with. Recalling Lagrangian description first, we then derive some basic but remarkable properties useful for the numerical computation of projected transport operators. We furthermore introduce new(More)