Volume 57, Number 4, July-August 2023
|Page(s)||2557 - 2593|
|Published online||03 August 2023|
A structure preserving hybrid finite volume scheme for semiconductor models with magnetic field on general meshes
Inria, Univ. Lille, CNRS, UMR 8524 – Laboratoire Paul Painlevé, F-59000 Lille, France
* Corresponding author: email@example.com
Accepted: 9 May 2023
We are interested in the discretisation of a drift–diffusion system in the framework of hybrid finite volume (HFV) methods on general polygonal/polyhedral meshes. The system under study is composed of two anisotropic and nonlinear convection–diffusion equations with nonsymmetric tensors, coupled with a Poisson equation and describes in particular semiconductor devices immersed in a magnetic field. We introduce a new scheme based on an entropy-dissipation relation and prove that the scheme admits solutions with values in admissible sets – especially, the computed densities remain positive. Moreover, we show that the discrete solutions to the scheme converge exponentially fast in time towards the associated discrete thermal equilibrium. Several numerical tests confirm our theoretical results. Up to our knowledge, this scheme is the first one able to discretise anisotropic drift–diffusion systems while preserving the bounds on the densities.
Mathematics Subject Classification: 65M08 / 35K51 / 35B40 / 35Q81 / 82D37
Key words: Finite volume schemes / General meshes / Anisotropic drift–diffusion equations / Semiconductor models / Poisson–Nernst–Planck system / Long-time behaviour / Entropy method
© The authors. Published by EDP Sciences, SMAI 2023
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