Application of the time discontinuous Galerkin finite element method to heat wave simulation

Abstract

This paper deals with the numerical simulation of heat wave propagation in the medium subjected to different kinds of heat source, particularly heat impulse. The discontinuous Galerkin finite element method (DGFEM) proposed for the stress wave propagation in solids [X.K. Li, D.M. Yao, R.W. Lewis, A discontinuous Galerkin finite element method for dynamic and wave propagation problems in non-linear solids and saturated porous media. Int. J. Numer. Meth. Eng. 57 (2003) 1775–1800] is extended to numerically solve for the non-Fourier heat transport equation constructed according to the CV model [C. Cattaneo, A form of heat-conduction equation which eliminates the paradox of instantaneous propagation, Compute Rendus 247 (1958) 431–433; P. Vernotte, Les paradoxes de la theorie continue de l’equation de la chaleur, Compute Rendus 246 (1958) 3154–3155]. Temperature and its time-derivative are chosen as primitive variables defined at each FE node. The main distinct characteristic of the proposed DGFEM is that the specific P3–P1 interpolation approximation, which uses piecewise cubic (Hermite’s polynomial) and linear interpolations for both temperature and its time-derivative, respectively, in the time domain is particularly proposed. As a consequence the continuity of temperature at each discrete time instant is exactly ensured, whereas discontinuity of the time-derivative of temperature at discrete time levels remains. Numerical results illustrate good performance of the present method in the numerical simulation of heat wave propagation in eliminating spurious numerical oscillations and in providing more accurate solutions in the time domain.