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A time discontinuous Galerkin finite element method for generalized thermo-elastic wave analysis, considering non-Fourier effects

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Abstract

Generalized thermo-elastic theory, which is based on the non-Fourier theory, indicates that there is a time delay between the heat flux vector and the temperature gradient. At present, the traditional numerical method for solving the thermo-elastic problem subjected to high-frequency heat source generally fails to properly capture discontinuities of impulsive waves in space and produces spurious numerical oscillations in the simulation of high modes and sharp gradients. In the paper, a time discontinuous Galerkin finite element method (DGFEM) for the solution of generalized thermo-elastic coupled problems is presented on the basis of well-known Lord–Shulman theory. The essential feature of the DGFEM is that the general temperature-displacement vector and its temporal gradient are assumed to be discontinuous and interpolated individually at each time level in time domain, respectively. In order to filter out the spurious wave-front oscillations, an artificial damping scheme is implemented in the final finite element formula. Numerical results show that the present DGFEM shows good abilities and provides much more accurate solutions for generalized thermo-elastic coupled behavior. It can capture the discontinuities effectively at the wave front and filter out the effects of spurious numerical oscillation induced by a high-frequency thermal shock.

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Authors and Affiliations

  1. The State Key Laboratory for Structural Analysis of Industrial Equipment, Department of Engineering Mechanics, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology, 116024, Dalian, China

    Pan Guo & Wen-Hua Wu

  2. The State Key Laboratory for Structural Analysis of Industrial Equipment, School of Aeronautics and Astronautics, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology, 116024, Dalian, China

    Zhi-Gang Wu

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  1. Pan Guo
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  2. Wen-Hua Wu
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  3. Zhi-Gang Wu
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Correspondence to Wen-Hua Wu.

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Guo, P., Wu, WH. & Wu, ZG. A time discontinuous Galerkin finite element method for generalized thermo-elastic wave analysis, considering non-Fourier effects. Acta Mech 225, 299–307 (2014). https://doi.org/10.1007/s00707-013-0961-8

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  • DOI: https://doi.org/10.1007/s00707-013-0961-8

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