A stable finite difference scheme for solving a hyperbolic two‐step model in a 3D micro sphere exposed to ultrashort‐pulsed lasers

Abstract

Purpose: To develop a numerical method for solving hyperbolic two‐step micro heat transport equations, which have attracted attention in thermal analysis of thin metal films exposed to ultrashort‐pulsed lasers.Design/methodology/approach: An energy estimation for the hyperbolic two‐step model in a three‐dimensional (3D) micro sphere irradiated by ultrashort‐pulsed lasers is first derived, and then a finite difference scheme for solving the hyperbolic two‐step model based on the energy estimation is developed. The scheme is shown to be unconditionally stable and satisfies a discrete analogue of the energy estimation. The method is illustrated by investigating the heat transfer in a micro gold sphere exposed to ultrashort‐pulsed lasers.Findings: Provides information on normalized electron temperature change with time on the surface of the sphere, and shows the changes in electron and lattice temperatures.Research limitations/implications: The hyperbolic two‐step model is considered under the assumption of constant thermal properties.Practical implications: A useful tool to investigate the temperature change in a micro sphere irradiated by ultrashort‐pulsed lasers.Originality/value: Provides a new unconditionally stable finite difference scheme for solving the hyperbolic two‐step model in a 3D micro sphere irradiated by ultrashort‐pulsed lasers.