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Article RSE 16004408

Stability of the discretization of the electron avalanche phenomenon


Journal of Computational Physics, vol. 296, pp. 369–381, Maggio-2015.

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R. Malgesini (RSE SpA) , A. Barbareschi Villa (RSE SpA), L. Barbieri (RSE SpA), M. Gondola (RSE SpA) , A. R. Leon-Garzon (Politecnico di Milano)

MON4-GRID 2015 - Management, monitoring and control of the transmission grid

In this work we focus on the transport-reaction equation that describe the evolution of electrons.

The numerical simulation of the discharge inception is an active field of applied physics with many industrial applications. In this work we focus on the drift-reaction equation that describes the evolution of the electrons. The main difficulty lies in the fact that the reaction term is positive when a high electric field is applied.

This leads exponentially growing solutions and this has a major impact on the behavior of numerical schemes. We analyze the stability of a reference finite volume scheme applied to this latter problem. The stability of the method may impose a strict mesh spacing therefore a proper stabilized scheme, which is stable whatever spacing is used, has been developed. The convergence of the scheme is treated as long as some numerical experiments.

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