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Old   July 28, 2012, 16:15
Default New to CFD need help
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Hi All

This is probably a very basic question but I'm a beginner in CFD and looking to get to grips with the fundementals, recently I've been developing basic 1D codes and now I wanna take in into 2D.

In the 1D forumations I've been constructing a matrix such that say for a central difference scheme

|AP AE aaaaaaa |
|AW AP AE aaaa |
|aa AW AP AE a | = A then solving A^-1*D=x
|aaaaaaaaaaaaa |
| aaaaaaaaaaaa |

Can I use a similar method to solve in 2D where I have values at the north and south nodes as well.
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Old   July 30, 2012, 01:06
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Quote:
Originally Posted by peterciaran View Post
Hi All

This is probably a very basic question but I'm a beginner in CFD and looking to get to grips with the fundementals, recently I've been developing basic 1D codes and now I wanna take in into 2D.

In the 1D forumations I've been constructing a matrix such that say for a central difference scheme

|AP AE aaaaaaa |
|AW AP AE aaaa |
|aa AW AP AE a | = A then solving A^-1*D=x
|aaaaaaaaaaaaa |
| aaaaaaaaaaaa |

Can I use a similar method to solve in 2D where I have values at the north and south nodes as well.
You can talk to the PDEs which discrete become the linear bellow!
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Old   July 31, 2012, 07:29
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Hi peterciaran. You are right, the procedure would be exactly the same when you go to a 2D problem with south and north nodes. The matrix would look like this:


|AP AE 0 0 0 ... AN ... |
|AW AP AE 0 0 .... AS ... AN ... |
|0 AW AP AE 0 .... AS ... AN ... |
|0 0 AW AP AE 0 ... AS ...AN ...|

I also suggest that you use the Thomas algotrith for your 1D problem instead of inverting the matrix, it will go much faster.

For the 2D problem I think you can use a line-by-line version of the Thomas algorithm, although I would suggest and iterative method (Gauss-Seidel for instance). This is all very well explained in Patankar's book (1980).

Cheers.
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Old   July 31, 2012, 09:48
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Quote:
Originally Posted by michujo View Post
Hi peterciaran. You are right, the procedure would be exactly the same when you go to a 2D problem with south and north nodes. The matrix would look like this:


|AP AE 0 0 0 ... AN ... |
|AW AP AE 0 0 .... AS ... AN ... |
|0 AW AP AE 0 .... AS ... AN ... |
|0 0 AW AP AE 0 ... AS ...AN ...|

There is a little mistake..
on a given line the matrix will rather look like:


0.....AS.......AW AP AE.......AN.....0
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Old   July 31, 2012, 17:07
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You are right.
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Old   August 1, 2012, 15:03
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If you are solving for a structured grid I would suggest using Beam-Warming ADI (Alternating Direction Implicit). Under some circumstances it does have a penalty of reduced CFL compared to direction inversion (thus more iterations), but it is faster per iteration and takes less memory. It is also straight forward to implement.
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