High accuracy stable numerical solution of 1D microscale heat transport equation

We investigate the use of a fourth-order compact finite difference scheme for solving a one-dimensional heat transport equation at the microscale.The fourth-order compact scheme is used with a Crank–Nicholson type integrator by introducing an intermediate function for the heat transport equation. The new scheme is proved to be unconditionally stable with respect to initial values. Numerical experiments are conducted to compare the new scheme with the existing scheme based on second-order spatial discretization. It is shown that the new scheme is computationally more efficient and more accurate than the second-order scheme. Copyright © 2001 John Wiley & Sons, Ltd.

[1]  C. L. Tien,et al.  Heat transfer mechanisms during short-pulse laser heating of metals , 1993 .

[2]  D. Tzou.  Experimental support for the lagging behavior in heat propagation , 1995 .

[3]  Murli M. Gupta,et al.  Symbolic derivation of finite difference approximations for the three‐dimensional Poisson equation , 1998 .

[4]  T. Qiu,et al.  Short-pulse laser heating on metals , 1992 .

[5]  Graham F. Carey,et al.  A high-order compact formulation for the 3D Poisson equation , 1996 .

[6]  Da Yu Tzou,et al.  The generalized lagging response in small-scale and high-rate heating , 1995 .

[7]  Jun Zhang.  Fast and High Accuracy Multigrid Solution of the Three Dimensional Poisson Equation , 1998 .

[8]  Graham F. Carey,et al.  Extension of high‐order compact schemes to time‐dependent problems , 2001 .

[9]  M. Lees,et al.  Alternating direction and semi-explicit difference methods for parabolic partial differential equations , 2018 .

[10]  Jun Zhang.  On convergence and performance of iterative methods with fourth‐order compact schemes , 1998 .

[11]  Murli M. Gupta,et al.  Comparison of Second- and Fourth-Order Discretizations for Multigrid Poisson Solvers , 1997 .

[12]  D. Tzou,et al.  On the Wave Theory in Heat Conduction , 1994 .

[13]  Weizhong Dai,et al.  A finite difference scheme for solving the heat transport equation at the microscale , 1999 .

[14]  G. Carey,et al.  High‐order compact scheme for the steady stream‐function vorticity equations , 1995 .

[15]  D. Tzou.  A Unified Field Approach for Heat Conduction From Macro- to Micro-Scales , 1995 .

[16]  Weizhong Dai,et al.  An unconditionally stable three-level explicit difference scheme for the Schro¨dinger equation with a variable coefficient , 1992 .

[17]  Arun Majumdar,et al.  Transient ballistic and diffusive phonon heat transport in thin films , 1993 .