期刊
INTERNATIONAL JOURNAL OF THERMAL SCIENCES
卷 49, 期 3, 页码 571-579出版社
ELSEVIER FRANCE-EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER
DOI: 10.1016/j.ijthermalsci.2009.08.007
关键词
Neumann (insulated) boundary condition; Heat conduction; Crank-Nicholson scheme; Higher-order scheme; Stability
The Neumann (or insulated) boundary condition is often encountered in engineering applications. The conventional finite difference schemes are either first-order accurate or second-order accurate but need a ghost point outside the boundary. Compact finite difference schemes are difficult to apply for multidimensional cases or for cylindrical and spherical coordinate cases. In this study, we present a kind of new and accurate finite difference schemes for the Neumann (insulated) boundary condition in Cartesian, cylindrical, and spherical coordinates, respectively. Combined with the Crank-Nicholson finite difference method or other higher-order methods, the overall scheme is proved to be unconditionally stable and provides much more accurate numerical solutions. The numerical errors and convergence rates of the solution are tested by several examples. Results show that the new method is promising. (C) 2009 Elsevier Masson SAS. All rights reserved.
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