Journal of Computational Physics
International Journal of Numerical Modelling: Electronic Networks, Devices and Fields
Journal of Scientific Computing
Least-squares spectral element method for non-linear hyperbolic differential equations
Journal of Computational and Applied Mathematics
Time-fractional heat equations and negative absolute temperatures
Computers & Mathematics with Applications
Hi-index | 7.29 |
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.