A second-order finite difference scheme for solving the dual-phase-lagging equation in a double-layered nanoscale thin film

详细信息    查看全文

• 作者：Hong Sun ; Zhi-zhong Sun and Weizhong Dai
• 刊名：Numerical Methods for Partial Differential Equations
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：33
• 期：1
• 页码：142-173
• 全文大小：941K
• ISSN：1098-2426

文摘

This article considers the dual-phase-lagging (DPL) heat conduction equation in a double-layered nanoscale thin film with the temperature-jump boundary condition (i.e., Robin's boundary condition) and proposes a new thermal lagging effect interfacial condition between layers. A second-order accurate finite difference scheme for solving the heat conduction problem is then presented. In particular, at all inner grid points the scheme has the second-order temporal and spatial truncation errors, while at the boundary points and at the interfacial point the scheme has the second-order temporal truncation error and the first-order spatial truncation error. The obtained scheme is proved to be unconditionally stable and convergent, where the convergence order in L ∞ -norm is two in both space and time. A numerical example which has an exact solution is given to verify the accuracy of the scheme. The obtained scheme is finally applied to the thermal analysis for a gold layer on a chromium padding layer at nanoscale, which is irradiated by an ultrashort-pulsed laser.