Third M.I.T. Conference on Computational Fluid and Solid Mechanics June 14–17, 2005  

Numerical discretization of a fully quantum drift-diffusion model

Pierre Degond, Samy Gallego, Florian Méhats*
MIP, Laboratoire CNRS (UMR 5640), Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex 04, France

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This paper is devoted to the discretization and numerical simulation of a new quantum drift-diffusion model that was derived recently. We define an implicit numerical scheme that is equivalent to a convex minimization problem and that preserves the physical properties of the continuous model: charge conservation, positivity of the density and dissipation of an entropy. We illustrate these results with some numerical simulations.

Keywords:  Quantum hydrodynamic models; Quantum drift-diffusion

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