A Discontinuous Finite Element Analysis of Transient Temperature Response in Semi-Transparent Media Induced by Pulsing Lasers

Abstract

A discontinuous Galerkin finite element formulation is presented for the simulation of the transient temperature distribution in a semi-transparent medium heated by an extra-fast pulsing laser. For this problem, the classic Fourier law breaks down and the thermal effects are described by a hyperbolic heat conduction equation coupled with internal radiative heat transfer. These coupled equations are solved using the discontinuous finite element method, which is particularly suited for problems of the hyperbolic type. In the paper, the discontinuous finite element formulation is presented and numerical fluxes are determined by enforcing the stability of the numerical method. Numerical analysis of the transient temperature response induced by a laser pulse is conducted for a one-dimensional semi-transparent slab with black boundaries. The numerical simulation demonstrates the non-Fourier characteristic of thermal wave behaviors in the slab, and the results from radiation-conduction coupling calculations show that the internal radiation helps to reduce the non-Fourier effects in the media.