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

Abstract

PurposeTo 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/approachAn 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.FindingsProvides 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/implicationsThe hyperbolic two‐step model is considered under the assumption of constant thermal properties.Practical implicationsA useful tool to investigate the temperature change in a micro sphere irradiated by ultrashort‐pulsed lasers.Originality/valueProvides a new unconditionally stable finite difference scheme for solving the hyperbolic two‐step model in a 3D micro sphere irradiated by ultrashort‐pulsed lasers.