Numerical analysis for hyperbolic heat conduction

A new numerical simulation of the hyperbolic heat conduction problem is investigated. The primary difficulty encountered in the numerical solution of such a problem is numerical oscillations in the vicinity of sharp discontinuities. In this work, it is shown that the hybrid technique based on the Laplace transform and control volume methods can successfully be applied to suppress these oscillations. The Laplace transform method is used to remove the time-dependent terms, and then the transformed equations are discretized by the control volume scheme. Various comparative examples involving a nonlinear problem with surface radiation and the hyperbolic heat conduction in a composite region are illustrated to verify the accuracy of the present method. Due to the application of the Laplace transform method, the present technique does not need to consider the effects of the Courant number on the numerical results.