Simulation of thermal disturbances with finite wave speeds using a high order method

The classical heat diffusion theory based on the Fourier’s model breaks down when considering transient heat flow, for short times, extreme thermal gradients or at low temperatures. The hyperbolic heat conduction equation based on the Cattaneo model for the heat flux incorporates a relaxation mechanism in order to gradually adjust to a change in the temperature gradient. A spectral element method is applied for solving the hyperbolic system treating the heat flux as an independent variable in addition to temperature. The numerical solution is based on the time-space least squares spectral method. Numerical examples are included for discussing the effects of the thermal waves.