A two-dimensional time-dependent heat transport equation at the microscale is derived. A second order finite difference scheme in both time and space is introduced and the unconditional stability of the finite difference scheme is proved. A computational procedure is designed to solve the discretized linear system at each time step by using a preconditioned conjugate gradient method. Numerical results are presented to validate the accuracy of the finite difference scheme and the efficiency of the proposed computational procedure.
|Number of pages||15|
|Journal||Journal of Computational Physics|
|State||Published - Jun 10 2001|
Bibliographical noteFunding Information:
1URL: http://www.cs.uky.edu/˜jzhang. The research of this author was supported in part by the U.S. National Science Foundation under Grants CCR-9902022, CCR-9988165, and CCR-0043861, and in part by the University of Kentucky Center for Computational Sciences. 2URL: http://www.umd.umich.edu/˜xich.
Copyright 2019 Elsevier B.V., All rights reserved.
- Crank-Nicholson integrator
- Finite difference scheme
- Heat transport equation
- Preconditioned conjugate gradient
ASJC Scopus subject areas
- Numerical Analysis
- Modeling and Simulation
- Physics and Astronomy (miscellaneous)
- Physics and Astronomy (all)
- Computer Science Applications
- Computational Mathematics
- Applied Mathematics