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Magnetic equations with FreeFem++: The Grad-Shafranov equation & the current hole

Erwan Deriaz, Bruno Despres, Gloria Faccanoni, Kirill Pichon Gostaf, Lise-Marie Imbert-Gérard, Georges Sadaka, Remy Sart (2011)

ESAIM: Proceedings

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...

Mathematical analysis of a spectral hyperviscosity LES model for the simulation of turbulent flows

Jean-Luc Guermond, Serge Prudhomme (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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...

Mathematical analysis of a spectral hyperviscosity LES model for the simulation of turbulent flows

Jean-Luc Guermond, Serge Prudhomme (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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...

Mathematical study of a petroleum-engineering scheme

Robert Eymard, Raphaèle Herbin, Anthony Michel (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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...

Mathematical study of a petroleum-engineering scheme

Robert Eymard, Raphaèle Herbin, Anthony Michel (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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...

Mixed finite element approximation for a coupled petroleum reservoir model

Mohamed Amara, Daniela Capatina-Papaghiuc, Bertrand Denel, Peppino Terpolilli (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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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