A numerical scheme for non-Fourier heat conduction, part I: One-dimensional problem formulation and applications

摘要

A simple and concise finite-difference algorithm is presented for the solution of non-Fourier one-dimensional heat conduction. The numerical algorithm is developed by applying the Godunov scheme on the characteristic equations that govern thermal waves within the medium. A vigorous investigation of the order of accuracy and stability of the procedure is presented. Several heat conduction problems are tested with the scheme, and the predicted temperature field is verified by comparing with results available in the literature. The accuracy of the solution is limited only by the selection of the mesh width in the space and time directions. The solution is free of oscillation, while the dissipation error associated with the numerical scheme in the wave front is controlled by specifying the proper Courant-Fredrichs-Lewy (CFL) condition. The algorithm provides a convenient, accurate, and efficient approximation to the hyperbolic heat conduction equation. It is evident that the procedure is beneficial for the study of propagation and reflection of thermal waves in solids. [References: 13]