Modeling and optimizing a road de-icing device by a nonlinear heating - Centre d'études et d'expertise sur les risques, l'environnement, la mobilité et l'aménagement Accéder directement au contenu
Article Dans Une Revue ESAIM: Mathematical Modelling and Numerical Analysis Année : 2019

Modeling and optimizing a road de-icing device by a nonlinear heating

Résumé

In order to design a road de-icing device by heating, we consider in the one dimensional setting the optimal control of a parabolic equation with a nonlinear boundary condition of the Stefan–Boltzmann type. Both the punctual control and the corresponding state are subjected to a unilateral constraint. This control problem models the heating of a road during a winter period to keep the road surface temperature above a given threshold. The one-dimensional modeling used in this work is a first step of the modeling of a road heating device through the circulation of a coolant in a porous layer of the road. We first prove, under realistic physical assumptions, the well-posedness of the direct problem and the optimal control problem. We then perform some numerical experiments using real data obtained from experimental measurements. This model and the corresponding numerical results allow to quantify the minimal energy to be provided to keep the road surface without frost or snow.
Fichier principal
Vignette du fichier
m2an180063.pdf (1.55 Mo) Télécharger le fichier
Origine : Publication financée par une institution
Loading...

Dates et versions

hal-02922759 , version 1 (26-08-2020)

Identifiants

Citer

Frederic Bernardin, Arnaud Munch. Modeling and optimizing a road de-icing device by a nonlinear heating. ESAIM: Mathematical Modelling and Numerical Analysis, 2019, 53 (3), pp.775-803. ⟨10.1051/m2an/2018056⟩. ⟨hal-02922759⟩
47 Consultations
28 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More