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Cite Details

R. Loubère, Une méthode particulaire lagrangienne de type Galerkin Discontinue. Application à la mécanique des fluides et l'interaction laser/plasma, PhD thesis, Université de Bordeaux, 2002

Abstract

A Discontinuous Galerkin type method written in Lagrangian coordinates is described in this work for unstructured meshes in 1D/2D for the Euler equations. By using Bernstein polynomials a diffusive process has been added to stabilize the method. Thanks to this process the Jacobian positivity is preserved during the computation ensuring the validity of the transformation from Euler coordinates to Lagrangian coordinates. The moment equations by respect to the Bernstein basis are solved. A Rieman solver (on moments) is used to treat the discontinuities between cells. Some numerical examples in compressible fluid dynamics show the efficiency of the method. This method has been adapted to the laser/plasma interaction domain by adding some source terms to the Euler equations.

BibTeX Entry

@phdthesis{loubere-2002-methode,
author = {R. Loub\`{e}re},
title = {Une m\'{e}thode particulaire lagrangienne de type Galerkin Discontinue. Application \`{a} la m\'{e}canique des fluides et l'interaction laser/plasma},
year = {2002},
urlpdf = {http://math.lanl.gov/Research/Publications/Docs/loubere-2002-methode.pdf},
school = {Universit\'{e} de Bordeaux}
}