GUILLARD , Hervé

Finite Volume upwind schemes for the Euler equations in the low Mach number regime face a problem of lack of convergence toward the solutions of the incompressible system. However, if applied to cell centered triangular grid, this problem disappears and convergence toward the incompressible solution is recovered. Extending the work of [3] that...

The derivation of reduced MHD models for fusion plasma is here formulated as a special instance of the general theory of singular limit of hyperbolic system of PDEs with large operator. This formulation allows to use the general results of this theory and to prove rigorously that reduced MHD models are valid approximations of the full MHD...

Finite Volume upwind schemes for the Euler equations in the low Mach number regime face a problem of lack of convergence toward the solutions of the incompressible system. However, if applied to cell centered triangular grid, this problem disappears and convergence toward the incompressible solution is recovered. Extending the work of [3] that...

For single phase fluid models, like the Euler equations of compressible gas dynamics, upwind finite volume schemes suffer from a loss of accuracy when computing flows in the near incompressible regime. Preconditioning of the numerical dissipation is necessary to recover results consistent with the asymptotic behaviour of the continuous model....

International audience

This work is devoted to a review of different modifications proposed to enable compressible flow solvers to compute accurately flows near the incompressible limit. First the reasons of the failure of upwind solvers to obtain accurate solutions in the low Mach number regime are explained. Then different correction methods proposed in the...

International audience

For single phase fluid models, like the Euler equations of compressible gas dynamics, upwind finite volume schemes suffer from a loss of accuracy when computing flows in the near incompressible regime. Preconditioning of the numerical dissipation is necessary to recover results consistent with the asymptotic behaviour of the continuous model....

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Les lagunes sont des systèmes complexes et essentiels qu'il convient de comprendre, en faisant appel aux mathématiques, afin d'aider à les préserver.

This work deals with the modeling of fusion plasma by bi-temperature fluid models. First, using non-dimensional scaling of the governing equations, we give the assumptions leading to a bi-temperature model. Then we describe a finite volume method on non-structured meshes to approximate the solutions of this model. The method relies on a...

We give a convergence estimate for a Petrov-Galerkin Algebraic Multigrid method. In this method, the prolongations are defined using the concept of smoothed aggregation while the restrictions are simple aggregation operators. The analysis is carried out by showing that these methods can be interpreted as variational Ritz-Galerkin ones using...

In the Magneto-HydroDynamic (MHD) equations, the magnetic field has to maintain a constraint of free-divergence. It exists two families of methods dealing with the free-divergence constraint. The first one consist to write the magnetic field as the curl of a potential vector. The second family is the divergence cleaning methods. This...

Reservoir simulation involves to compute dynamic flow of different phases ina porous medium. The initial state of the reservoir is usually precomputed viageo-statistics methods, extrapolating measures of the terrain. so, the inputof reservoir simulation is given as a fine mesh containing heterogeneous dataIn this paper, we describe an...

We give a convergence estimate for a Petrov-Galerkin Algebraic Multigrid method. In this method, the prolongations are defined using the concept of smoothed aggregation while the restrictions are simple aggregation operators. The analysis is carried out by showing that these methods can be interpreted as variational Ritz-Galerkin ones using...

In this paper are analyzed finite element methods based on Powell-Sabin splines, for the solution of partial differential equations in two dimensions. PS splines are piecewise quadratic polynomials defined on a triangulation of the domain, and exhibit a global C 1 continuity. Critical issues when dealing with PS splines, and described in this...

Nuclear fusion is one promising way to produce a clean energy in the forthcoming years. The possibility to construct nuclear fusion reactors is studied in large scale physics experiments as the international ITER project in construction in Cadarache, France that gathers contributions from seven different countries. In this experimental reactor,...

This paper describes an algorithm designed for the automatic coarsening of three-dimensional unstructured simplicial meshes. This algorithm can handle very anisotropic meshes like the ones typically used to capture the boundary layers in CFD with Low Reynolds turbulence modeling that can have aspect ratio as high as 104. It is based on the...

In the last recent years, thanks to the increasing power of the computational machines , the interest in more and more accurate numerical schemes is growing. Methods based on high-order approximations are nowadays the common trend in the computational research community, in particular for CFD applications. This work is focused on Powell-Sabin...

This paper gives a derivation of the two-temperature Euler plasma system from the two-fluid MHD model. The two-temperature Euler plasma system is proved to be an asymptotic regime for weakly magnetized plasma of the two-fluid MHD model. Our procedure is more general, enabling us to show that assumptions in previous derivations in literature are...

Dans les tokamaks comme ITER, la matière est à l'état de plasma chaud en interaction avec des ondesélectromagnétiques. La modélisation et la simulation numérique du transport des électrons et des ions,particules chargées qui constituent ce plasma, sont un processus-clé de la réussite de ce projet.La dynamique des particules chargées peut être...

International audience

An extension and numerical approximation of the shear shallow water equationsmodel recently proposed in [21] is considered in this work. The model equations are able todescribe the oscillatory nature of turbulent hydraulic jumps and as such correct the deficiency ofthe classical shallow water equations in describing...

In this paper is presented a Powell-Sabin finite-elements scheme (PS-FEM) for the solution of the 2D Euler equations in supersonic regime. The spatial dis-cretization is based on PS splines, that are piecewise quadratic polynomials with a global C 1 continuity, defined on conforming triangulations. Some geometrical issues related the practical...

Numerical simulations of the magnetohydrodynamics (MHD) equations have played a significant role in plasma research over the years. The need of obtaining physical and stable solutions to these equations has led to the development of several schemes, all requiring to satisfy and preserve the divergence constraint of the magnetic field...