CFD Online Logo CFD Online URL
www.cfd-online.com
[Sponsors]
Home > Forums > General Forums > Main CFD Forum

How to enforce positive values

Register Blogs Members List Search Today's Posts Mark Forums Read

Like Tree1Likes
  • 1 Post By John C. Chien

Reply
 
LinkBack Thread Tools Search this Thread Display Modes
Old   July 31, 2000, 17:48
Default How to enforce positive values
  #1
Ning
Guest
 
Posts: n/a
I am solving a concentration equation with the NS equations. Everthing is fine except that, occationally, the concentration values become negative in the area where the value should be very small. I am looking for a method which can numerically enforce the positive requirment. Any suggestion or reference is highly appreciated.
  Reply With Quote

Old   July 31, 2000, 18:33
Default Re: How to enforce positive values
  #2
Kalyan
Guest
 
Posts: n/a
There are advection-diffusion schemes which enforce the positivity condition on the scalar variables in simulations. I do not have a reference with me right now, but you can search in the Journal of Comp. Phys. index using strings "positive" & "scheme" in the title.

If you have difficulty finding any of these papers, I can try to search for one I had copied long time ago.
  Reply With Quote

Old   July 31, 2000, 23:29
Default Re: How to enforce positive values
  #3
istadi
Guest
 
Posts: n/a
Please describe completely about governing equations that you should be solved. Do you involve a convection-diffusion problem or diffusion only ? If you have a problem with convection-diffusion, it is more complex than diffusion only. So, you must take care about boundary condition about linearization or others. Thanks
  Reply With Quote

Old   August 1, 2000, 06:30
Default Re: BALDWIN -LOMAX mixing length turbulence model
  #4
John Akoll
Guest
 
Posts: n/a
I am a newcomer to CFD and presentlt I am trying to write the Baldwin -lomax mixing length turbulence model .could somebody give me ideas and possibly an algorithm that I can use to implement the model.

Thanks

John
  Reply With Quote

Old   August 1, 2000, 15:33
Default Re: How to enforce positive values
  #5
Patrick Godon
Guest
 
Posts: n/a
A simple way is just to solve for the log of the function rather than for the function itself.

I am presently doing this for the density and internal energy in the Full Navier-Stokes Equations. I have changes in density or many orders of magnitude and the best way to avoid sharp gradient, small quantities, negative quantities is to use the log of the function. So I am solving for log(rho) where rho is the density and log(e) where e=3/2NkT is the internal energy of the gas. In my case the equations are actually simpler (they have a simpler form) than using the original functions themselves.

For sure you will NEVER get a Negative value, since log is a positive function.

I hope this can help.

Patrick Godon
  Reply With Quote

Old   August 2, 2000, 11:46
Default Re: How to enforce positive values
  #6
Ning
Guest
 
Posts: n/a
After comparing several methods, I find this one more interesting. Would you please show me some detail? I am solving a convection-diffusion equation of a concertration field together with NS equations. The equation looks like: (for simplicity, in 1D form)

dc/dt + u*dc/dx = d/dx(k*dc/dx))

What is the equation of log(c) look like? I am not quite sure whether or not the sequence of log operation and derivitives can be changed. Also, I have to model the diffusivity k, which is not a constant. Does this matter?

Thanks

  Reply With Quote

Old   August 2, 2000, 12:11
Default Re: How to enforce positive values
  #7
Patrick Godon
Guest
 
Posts: n/a
Hi,

Thank you for your interest in my suggestion.

let f = log(c) ; then c = dexp(f)

In Fortran for example alog and dexp are the functions you need and are in basis e (natural logarithmic) NOT in basis 10. So you can keep the basis e, that's just fine.

Then you differentiate:

dc/dx=c * df/dx

and again

d2c/dx2 = dc/dx*df/dx+c*d2f/dx2 =

= c*(df/dx)**2 + c*(d2f/dx2)

Then you put all this back in the original equation (the same hold for time derivatives):

c*df/dt+u*c*df/dx=c*dk/dx*df/dx+k*c*(df/dx)**2+k*c*(d2f/dx2) ,

where d/dx(k*dc/dx)=dk/dx*dc/dx +k*d2c/dx2

Now you can divide by c (if c is not zero) and get an new equation for f:

df/dt+u*df/dx=dk/dx*df/dx+k*(df/dx)**2+k*(d2f/dx2) ,

and you notice that the equation does not even include f, but only its derivatives! So the equation is even simpler. This might be a little different if you have other terms where c does not appear, because then you will get terms like 1/c that you need to write 1/dexp(f). The difficult part is probably just to pay attention and to replace c correctly everywhere else c=dexp(f).

And the results are wonderfull, you can get extremely small value for c!

Cheers,

Patrick Godon
  Reply With Quote

Old   August 2, 2000, 14:40
Default Re: How to enforce positive values
  #8
Ning
Guest
 
Posts: n/a
Thank you very much. Your method is very practical. I will extend it to 3D situation and apply to my computation. Thanks again.
  Reply With Quote

Old   August 14, 2000, 20:01
Default Re: How to enforce positive values
  #9
Bernard Parent
Guest
 
Posts: n/a
Interesting, but your scheme is non conservative anymore, i.e. a finite volume method discretizing the 'c' mass conservation equation in log form will not guarantee mass to be conserved.. So in assuring positive values of 'c' you lose the conservative property of the scheme..

Or am I mislead?

-bernard
  Reply With Quote

Old   August 16, 2000, 14:53
Default Re: How to enforce positive values
  #10
Patrick Godon
Guest
 
Posts: n/a
I am using a high order accuracy method and still conserve quantities. But of course depending on the method you are using you can have trouble conserving some quantities. THere are given forms used to conserve momentum for example, where you solve for the momenta rather than velocities; or to conserve energy where you include the kinetic energy , etc.. All this is a matter of taste. For sure if you have a problem of negative pressure and negative density you will first be conerned with that and only after that you will want to worry about concerving the mass. You will need to check for the specific problem that you are solving to see where and how much mass is not concerved, if this can be neglected or if you find a better approach, etc... You might want to introduce rectification terms or geometric terms to help conserve quantities.
  Reply With Quote

Old   August 20, 2000, 01:10
Default Re: How to enforce positive values
  #11
John C. Chien
Guest
 
Posts: n/a
(1). You have to tell the system that the concentration value must be on the positive side. Since you did not include this property in the formulation, it is possible to get the negative value. (2). So, getting the negative value is normal. (it is like an organization without a cfd department and trying to run cfd codes, most of the time, they are going to get diverged solutions or wrong solutions. I am using this example, because I have been studying the failure modes of angineering organizations.) So, it is important to have someway to correct the course, that is to have human interaction with the codes. (3). Therefore, if you are looking for non-negative solutions, you must include this constraint in the formulation. It shouldn't be difficult to throw out the negative values in the calculation. As a matter of fact, it is a good idea to set a minimum possible level for the concentration. (4). In most applications, the concentration is normalized to one at the inlet, in this way, you have a cut-off value relative to one to follow. The convection and the diffusion of the concentration should not cause the value to become negative. And if for any reason, it becomes negative, you can use the lower limit to correct the behavior. It is also a good idea to find out "why" the concentration is getting negative values. (5). For reacting flows, it is another story. But the same principle applies. I would say that higher-order schemes tends to produce numerical wiggles in a convection-diffusion system. In this case, you will have to refine the mesh until the wiggles are gone. Otherwise, higher-order scheme will simply create non-physical solutions. (6). This is the basic limitation of the finite-difference or finite-volume methods. Unless you re-invent new physics, it is hard to get the real solutions with finite size mesh. Something has to give.
randolph likes this.
  Reply With Quote

Reply

Thread Tools Search this Thread
Search this Thread:

Advanced Search
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are Off
Pingbacks are On
Refbacks are On


Similar Threads
Thread Thread Starter Forum Replies Last Post
TimeVaryingMappedFixedValue irishdave OpenFOAM Running, Solving & CFD 32 June 16, 2021 07:55
max node values exceed max element values in contour plot jason_t FLUENT 0 August 19, 2009 12:32
exact face values RubenG Main CFD Forum 0 June 22, 2009 12:09
strange node values @ solid/fluid interface - help JB FLUENT 2 November 1, 2008 13:04
How to confine scalar to positive values Sheila Siemens 5 February 1, 2005 15:06


All times are GMT -4. The time now is 03:41.