New to CFD need help

peterciaran · July 28, 2012, 17:15

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.

vanchanh123 · July 30, 2012, 02:06

Quote:

Originally Posted by peterciaran

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!

michujo · July 31, 2012, 08:29

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.

leflix · July 31, 2012, 10:48

Quote:

Originally Posted by michujo

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

michujo · July 31, 2012, 18:07

You are right.

Martin Hegedus · August 1, 2012, 16:03

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.

July 28, 2012, 17:15	New to CFD need help	#1
peterciaran New Member Join Date: Jul 2012 Posts: 2 Rep Power: 0	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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July 31, 2012, 08:29		#3
michujo Senior Member Join Date: Dec 2011 Location: Madrid, Spain Posts: 134 Rep Power: 15	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.

July 31, 2012, 18:07		#5
michujo Senior Member Join Date: Dec 2011 Location: Madrid, Spain Posts: 134 Rep Power: 15	You are right.

August 1, 2012, 16:03		#6
Martin Hegedus Senior Member Martin Hegedus Join Date: Feb 2011 Posts: 500 Rep Power: 19	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.