Numerical analysis for the hyperbolic heat conduction problem under a pulsed surface disturbance

Abstract

A hybrid application of the Laplace transform method and a control-volume formulation in conjunction with the hyperbolic shape functions is applied to investigate the hyperbolic diffusion problems with the pulsed boundary conditions in various coordinate systems. The Laplace transform method is used to remove the time-dependent terms in the governing differential equations and the boundary conditions, and then the transformed equations are discretized by the control volume scheme. The primary difficulty in dealing with the present problem is the suppression of numerical oscillations in the vicinity of sharp discontinuities. The results show that the numerical results agree well with the analytic solution and do not exhibit numerical oscillations in the vicinity of the jump discontinuity. The present method also can solve the problems with the singular point.