Investigation on the Use of a Spacetime Formalism for Modeling and Numerical Simulations of Heat Conduction Phenomena

  • 1 Université de Technologie de Troyes (UTT), Institut Charles Delaunay (ICD), Laboratoire des Systèmes Mécaniques et d’Ingénierie Simultanée (LASMIS), Troyes, France
  • 2 Safran, Modelling & Simulation department, Magny les hameaux, France
  • 3 Université Pierre et Marie Curie, Paris, France
Roula Al Nahas
  • 27093Université de Technologie de Troyes (UTT), Institut Charles Delaunay (ICD), Laboratoire des Systèmes Mécaniques et d’Ingénierie Simultanée (LASMIS), Troyes, France
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, Alexandre Charles, Benoît PanicaudORCID iD: https://orcid.org/0000-0001-6814-7090, Emmanuelle Rouhaud
  • 27093Université de Technologie de Troyes (UTT), Institut Charles Delaunay (ICD), Laboratoire des Systèmes Mécaniques et d’Ingénierie Simultanée (LASMIS), Troyes, France
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, Israa Choucair
  • 27093Université de Technologie de Troyes (UTT), Institut Charles Delaunay (ICD), Laboratoire des Systèmes Mécaniques et d’Ingénierie Simultanée (LASMIS), Troyes, France
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, Kanssoune Saliya
  • 27093Université de Technologie de Troyes (UTT), Institut Charles Delaunay (ICD), Laboratoire des Systèmes Mécaniques et d’Ingénierie Simultanée (LASMIS), Troyes, France
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and Richard Kerner

Abstract

The question of frame-indifference of the thermomechanical models has to be addressed to deal correctly with the behavior of matter undergoing finite transformations. In this work, we propose to test a spacetime formalism to investigate the benefits of the covariance principle for application to covariant modeling and numerical simulations for finite transformations. Several models especially for heat conduction are proposed following this framework and next compared to existing models. This article also investigates numerical simulations using the heat equation with two different thermal dissipative models for heat conduction, without thermomechanical couplings. The numerical comparison between the spacetime thermal models derived in this work and the corresponding Newtonian thermal models, which adds the time as a discretized variable, is also performed through an example to investigate their advantages and drawbacks.

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