Dear friends, I am trying to solve a transient 3dD conduction problem in cylindrical coordinates. To solve the set of algebraic equations obtained i tried to use the ADI method. Unfortunately till now the results are bad. Can someone help me with reference (i have books about this topic but in 2D which is quite different), any article close to my topic will be very helpfull for me.

Thank you very much for your help

ADI in 3-D is NOT an unconditional stable scheme, although its 2-D version is. There was a revised version of 3-D ADI but I just can remember where to find it. You may try another solver.

HLI

There are a couple of ancient references that gave usable algorithms when I used them last (1971!). Take a look at:

J. Douglas, "Alternating Direction Methods for Three Space Variables," Numerische Mathematik, v. 4, pp. 41-63 (1962).

I actually used the following:

P. L. T. Brian, "A Finite-Difference Method of High-Order Accuracy for the Solution of Three-Dimensional Transient Heat Conduction Problems," AIChE Journal, v. 7, pp. 367-370 (1961).

Good Luck!

Jim

yes ADI should work well for this problem if you remember that it is not unconditionally stable. also it isn't easy to program. i found this out when i tried a 2D problem in rectangular coordinates using this method. personally i recommend Alternating Directions explicit (ADE) scheme (see Tannehill, Anderson, and Pletcher's CFD book) it is easy to code and is unconditionally stable (at least in 2D)