A general formulation of Peaceman and Rachford Adi method for the N-dimensional heat diffusion equation

✍ Scribed by Cheng Gao; Yansheng Wang

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 369 KB
• Volume: 23
• Category: Article
• ISSN: 0735-1933
• DOI: 10.1016/0735-1933(96)00067-x

✦ Synopsis

A general formulation of an alternating direction implicit (ADI) method was derived by extending Peaceman and Rachford scheme from two-dimensions to a Ndimensional space (N _> 2). The von Neumann stability analysis was performed to obtain a simple explicit stability criterion which takes a general form of r= aAt/du: <_ N/2(N-2).

For N = 2, the scheme is unconditional stable while for N _> 3, the scheme becomes conditional stable. A non-negative coefficient criterion was discussed which is more stricter than the stability criterion, but both of them approach 1/2 as a limit when N ~ oo. The running time for the algorithm implementation of the general ADI scheme is 0 N m, while the computational storage is 0 m, , where m,. is the number of temperature nodes in i~h spatial "t l 1 direction.