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...

We analyse a multi-level method based on successive projections of descent directions into vector spaces os smaller dimensions than the original space. We first show that the original space can be splitted into a direct sum (in the sense of the energy norm) of n+1 orthogonal spaces where n is the number of levels. Using this result, we then...

For finite-element non-structured type meshes, the non-nested multigrid algorithms require to build a sequence of independent meshes. The paper proposes an automatic way to generate the coarse meshes given the finest one. The method first eliminates a set of points from the current mesh level and then uses the Delaunay-Voronoi algorithm to...

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. We give here a general proof of...

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...

Using the defect correction method (DeC), we propose an implicit scheme that is second order accurate both in time and space,but that uses only first order jacobian. In a first time, we theoretically analyse the truncation error of the scheme and perform a linear stability analysis of it. Then some numerical experiments over simple test-cases...

This paper presents an asymptotic analysis in power of the Mach number of the flux difference splitting approximation of the compressible Euler equations in the low Mach number limit. We prove that the solutions of the discrete system contain pressure fluctuations of order $Ma$ while the continuous pressure scales with the square of the Mach...

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This paper studies an Eulerian diffuse interface model for the simulation of compressible multifluid and two-phase flow problems. We first show how to derive this model from a seven equation, two pressure, two velocity model of Baer-Nunziato type using an asymptotic analysis in the limit of zero relaxation time. We then study the mathematical...