A finite difference scheme for solving a nonlinear hyperbolic two-step model in a double-layered thin film exposed to ultrashort-pulsed lasers with nonlinear interfacial conditions

Hyperbolic two-step microscale heat transport equations have attracted attention in thermal analysis of thin metal films exposed to ultrashort-pulsed lasers. Exploration of temperature-dependent thermal properties is absolutely necessary to advance our fundamental understanding of microscale (ultrafast) heat transport. In this article, we develop a finite difference scheme, by obtaining an energy estimate, for solving the hyperbolic two-step model with temperature-dependent thermal properties in a double-layered microscale thin film with nonlinear interfacial conditions irradiated by ultrashort-pulsed lasers. The method is illustrated by investigating the heat transfer in a gold layer on a chromium layer.