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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.
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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