Journal
JOURNAL OF NON-EQUILIBRIUM THERMODYNAMICS
Volume 45, Issue 3, Pages 223-246Publisher
WALTER DE GRUYTER GMBH
DOI: 10.1515/jnet-2019-0074
Keywords
spacetime modeling; constitutive models; covariance principle; projectors; spacetime thermodynamics; hyperbolic heat conduction; finite propagation; weak integral form
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Funding
- European Regional Development Funds (FEDER)
- Safran Tech company
- region Grand Est of France
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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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