Numerical analysis of the hyperbolic two-temperature model

Abstract

The system of hyperbolic heat conduction problems is solved numerically. The explicit and fully implicit Euler type schemes for the time integration of the nonstationary problem are proposed and investigated. Space derivatives are approximated by using the finite volume method, resulting in conservative and monotonous discrete approximations of the second order of accuracy. The stability analysis is done in the L2 and energy norms for a simplified one-temperature equation and the system of two equations, describing the temperature and the flux. Results of numerical experiments are presented.