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A Coherent Derivation of an Average Ion Model Including the Evolution of Correlations Between Different Shells

Daniel Bouche;  Alain Decoster;  Laurent Desvillettes;  Valeria Ricci — 2013

MathematicS In Action

We propose in this short note a method enabling to write in a systematic way a set of refined equations for average ion models in which correlations between populations are taken into account, starting from a microscopic model for the evolution of the electronic configuration probabilities. Numerical simulations illustrating the improvements with respect to standard average ion models are presented at the end of the paper.

Theoretical analysis of the upwind finite volume scheme on the counter-example of Peterson

Daniel Bouche;  Jean-Michel Ghidaglia;  Frédéric P. Pascal — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

When applied to the linear advection problem in dimension two, the upwind finite volume method is a non consistent scheme in the finite differences sense but a convergent scheme. According to our previous paper [Bouche , (2005) 578–603], a sufficient condition in order to complete the mathematical analysis of the finite volume scheme consists in obtaining an estimation of order , less or equal to one, of a quantity that depends only on the mesh and on the advection velocity...

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