Space–time Galerkin methods for simulation of laser heating using the generalized nonlinear model

Wakeni, M.F. and Reddy, B.D. (2019) Space–time Galerkin methods for simulation of laser heating using the generalized nonlinear model. Computer Methods in Applied Mechanics and Engineering, 357, 112586. (doi: 10.1016/j.cma.2019.112586)

Abstract

The generalized thermal model is a thermodynamically consistent extension of the classical Fourier’s law for describing thermal energy transportation which is very relevant to applications involving very small length, time scales and/or at extremely low temperatures. Under such conditions, thermal propagation has been observed to manifest as waves, a phenomenon widely referred to as second sound effect. However, this is in contrast to the paradoxical prediction of the Fourier’s model that thermal disturbances propagate with infinite speed. In this work, we review the nonlinear model based on the theory of Green and Naghdi for thermal conduction in rigid bodies and present its implementation within a class of space–time methods. The unconditional stability of the time-discontinuous Galerkin method without restriction over the grid structure of the space–time domain is proved. We also perform a number of numerical experiments to study the convergence properties and analyze the thermal response of materials under short-pulsed laser heating in two space dimensions.

• Item Type: Articles
• Additional Information: The work reported in this paper has been supported by the National Research Foundation of South Africa through the South African Research Chair in Computational Mechanics.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Wakeni, Dr Mebratu
• Authors: Wakeni, M.F., and Reddy, B.D.
• College/School: College of Science and Engineering > School of Engineering > Infrastructure and Environment
• Journal Name: Computer Methods in Applied Mechanics and Engineering
• Publisher: Elsevier
• ISSN: 0045-7825
• ISSN (Online): 1879-2138
• Published Online: 17 August 2019
• Copyright Holders: Copyright © 2019 Elsevier B.V.
• First Published: First published in Computer Methods in Applied Mechanics and Engineering 357:112586
• Publisher Policy: Reproduced in accordance with the publisher copyright policy