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August 16, 1999, 23:32 
artificial compressiblity?(pressure)

#1 
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hi, it is a typical problem.. i read Chorin's paper,"a numerical method for solving incompressible viscous flow.", about artificial compressiblity methods. i coded following the direction.i velocity field exactly, but didn't pressure field.i checked the program a few times, there is no error.
i used pressure this way. p=rho/delta p: pressure rho : artificial density delta: artificial compressibility (=0.00032 as paper sais) bye.. 

August 17, 1999, 00:20 
Re: artificial compressiblity?(pressure)

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(1). Someone at NASA/ames and Rockwell/ Rocketdyne (now Boeing/Rocketdyne) used to work on 3D incompressible flows using this method, back in mid 80's. (2). You can search AIAA journal for publications in this area, or get in touch with someone at NASA/ames research center. It was laminar flow calculations, as I recall.


August 17, 1999, 15:30 
Re: artificial compressiblity?(pressure)

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I know that NASA has a CFD code based on artificial compressibility called INS2D and INS3D where INS stands for Incompressible NavierStokes. This is a pretty well established method and a lot of work has been done in this area so that a commerciallike code came out of it. I vaguely recall the name of one of the top persons in this group to be Kwak.
I myself did a very small amount of work in this area for a graduate level course project to find out what exactly Lee has found. I used it for 'channel flow' to find the velocity field to be o.k. whereas the pressure was truely checkerboard type. For 'cavity problem' without any inflow or outflow I again got decent velocity field. I did not have any experimental pressure field to compare my prediction against. I did not have the opportunity to continue reasearch in this area any further. Again there is nothing new about this method. There is a lot of material out there if someone is truely interested. There is also User's Manual and Methodology for the NASA's INS codes. There are also plenty of publication by Kwak(?) and his group in aerospace related journals. Hope this helps! 

August 17, 1999, 17:08 
Re: artificial compressiblity?(pressure)

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Thanks Chien and Hussain, it is a channel flow.
Channel is square, 0<=x<=1, 0<=y<=1. The velocity is u=y(1y)/4 v=0 at x=0 and x=1. the exact solution is u=y(1y)/4 v=0 p=cx where c is arbitrary constant in all domain. u and v , i get, is predicted exactly and the trend of pressure, which p is only function of x, is correct. but the magnitude is too big, from 3.8 to 3.8. the pressure at instream is 3.8 and 3.8 at outstream. i was wondering that the pseudocompressiblity has the limitation of pressure prediction. thanks ahead. 

August 18, 1999, 01:59 
Re: artificial compressiblity?(pressure)

#5 
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(1). I did not work on this fancy method. (2). But in your test case, you can just use the exact analytical solution for u and v , and substitute u and v into the method. In this way, you can easily check out the formulation for the pressure portion of solution. (3). Actually, the test case is 1D problem. So, why not just look at the 1D part of the pressure solution. In this way, you should be able to tell whether this method is all right or not for the pressure solution. If it can not solve a simple 1D problem, the the answer is clear.


August 18, 1999, 20:14 
Re: artificial compressiblity?(pressure)

#6 
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Lee,
I would check and see if the pressure gradients are correct. Since the pseudocompressibility method is based on the incompressible equations the value of pressure used by the code is only important to provide an accurate calculation of its gradient. The coeficient used in the continuity equation for timemarching is optimized for faster convergence and not as a reflection of the true value of the pressure. Since you say the pressure trend is correct (by that I suppose the pressure gradients are similar to the experimental data) the algorithm is working as intended. Hope I helped, Paulo 

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