Alternating-direction implicit method: Difference between revisions

Revision as of 11:15, 8 August 2008

Revision as of 02:42, 17 November 2008

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where <math>\delta_p^2</math> is the central difference operator for the ''p''-coordinate.

After performing a stability analysis, it can be shown that this method will be stable asfor longany asr.

: <math>{\Delta t \over (\Delta x)^2}+{\Delta t\over (\Delta y)^2} < {1 \over 2}.</math>

But problem is the final matrix to solve is not tridiagonal, but is banded. Depending on the ordering (the numbering of the points), the bandwidth of matrix can be very large, and this causes the solution procedure to be more difficult.

This an unaffordable numerical stability criterion.

The idea behind the ADI method is to split the finite difference equations into two, one with the x-derivative taken implicitly and the next with the y-derivative taken implicitly,