A SPACE–TIME CE/SE METHOD FOR SOLVING HYPERBOLIC HEAT CONDUCTION MODEL

Abstract

This paper is concerned with the numerical approximation of one and two-dimensional models describing heat conduction in solids at low temperature. The system contains a conservation equation for the energy density and balance equations for the heat fluxes along each characteristic direction. A conservation element and solution element method (CE/E) is proposed for solving the given model. The method has already shown its efficiency and accuracy for solving a wide range of engineering problems. This technique is considerably different in both logic and design from the well-established finite volume schemes. The scheme treats space and time in a unified manner where conserved variables and their gradients are considered as independent unknowns. To illustrate the performance of the CE/SE method, several one and two-dimensional numerical case studies are carried out. The results of kinetic flux vector splitting (KFVS) scheme and central scheme are also presented for the comparison and further validation of our numerical results. The computations of this paper demonstrates that CE/SE method is effective in handling such problems.