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FreeFem++ [11] is a software for the numerical solution of partial differential
equations. It is based on finite element method. The FreeFem++ platform aims at
facilitating teaching and basic research through prototyping. For the moment this platform
is restricted to the numerical simulations of problems which admit a variational
formulation. Our goal in this work is to evaluate the FreeFem++ tool on basic magnetic
equations arising in Fusion Plasma...
This paper presents a model based on spectral hyperviscosity for the simulation of 3D turbulent incompressible flows. One particularity of this model is that the hyperviscosity is active only at the short velocity scales, a feature which is reminiscent of Large Eddy Simulation models. We propose a Fourier–Galerkin approximation of the perturbed Navier–Stokes equations and we show that, as the cutoff wavenumber goes to infinity, the solution of the model converges (up to subsequences) to a weak solution...
This paper presents a model based on spectral hyperviscosity for the
simulation of 3D turbulent incompressible flows. One particularity of this
model is that the hyperviscosity is active only at the short velocity scales,
a feature which is reminiscent of Large Eddy Simulation models.
We propose a Fourier–Galerkin approximation of the perturbed
Navier–Stokes equations and we show that, as the cutoff wavenumber
goes to infinity, the solution of the model
converges (up to subsequences) to a weak...
Models of two phase flows in porous media, used in petroleum engineering, lead to a system of two coupled equations with elliptic and parabolic degenerate terms, and two unknowns, the saturation and the pressure. For the purpose of their approximation, a coupled scheme, consisting in a finite volume method together with a phase-by-phase upstream weighting scheme, is used in the industrial setting. This paper presents a mathematical analysis of this coupled scheme, first showing that it satisfies...
Models of two phase flows in porous media, used in petroleum
engineering, lead to a system of two coupled equations with elliptic
and parabolic degenerate terms, and two unknowns,
the saturation and the pressure.
For the purpose of their approximation, a coupled scheme, consisting in
a finite volume method together with
a phase-by-phase upstream weighting scheme, is used in the industrial setting.
This paper presents a mathematical analysis of this coupled scheme, first showing
that it satisfies...
In this paper, we are interested in the modelling and the finite element approximation of a petroleum reservoir, in axisymmetric form. The flow in the porous medium is governed by the Darcy-Forchheimer equation coupled with a rather exhaustive energy equation. The semi-discretized problem is put under a mixed variational formulation, whose approximation is achieved by means of conservative Raviart-Thomas elements for the fluxes and of piecewise constant elements for the pressure and the temperature....
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