ON THE NUMERICAL SOLUTION OF HYPERBOLIC HEAT CONDUCTION

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Abstract
Non-Fourier heat conduction is governed by the hyperbolic heat conduction equation, which involves the wave nature of thermal energy transport. In such cases, energy propagates in the medium as a wave with sharp discontinuities at the wave front. Difficulties encountered in the numerical solution of such problems include, among others, numerical oscillations and the representation of sharp discontinuities with good resolution at the wave front. In this work it is shown that a numerical technique based on MacCormack's predictor-corrector scheme can be used to handle discontinuities at the wave front with high resolution and little oscillation. Numerical predictions are compared with the exact analytic solutions for a wide variety of strict test conditions. For all the cases considered, the present numerical scheme remains stable and produces high resolution at the sharp wave front.

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