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

additional variable in diffusion-trasnport equation

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

Reply
 
LinkBack Thread Tools Display Modes
Old   June 20, 2013, 07:48
Default additional variable in diffusion-trasnport equation
  #1
mva
New Member
 
Maria
Join Date: Jun 2013
Posts: 3
Rep Power: 4
mva is on a distinguished road
Hi

I am trying to model cell diffusion in a cube 1x1. I have defined concentration as additional variable and solve it as diffusion transport equation. However I want to solve a non-linear diffusion equation which has a form as shown in the attached file.
I have defined the whole cube as a subdomain apart from the upper surface in which I have assigned inlet boundary condition as (concentration) c=1. The other surfaces of the domain are set as walls with zero flux.
In the subdomain I have defined as source to be concentration^2. Since the diffusion-transport equation also includes density I have set the domain to be consisted of a material with density =1. However for an internal point far from the boundary I take even for t=0, cell concentrations only higher than 1 which is not reasonable.
I have no experience in working with ANSYS so could you please help me.

Thank you in advance.
Attached Files
File Type: docx equation.docx (14.9 KB, 15 views)
mva is offline   Reply With Quote

Old   June 20, 2013, 18:49
Default
  #2
Super Moderator
 
Glenn Horrocks
Join Date: Mar 2009
Location: Sydney, Australia
Posts: 10,646
Rep Power: 84
ghorrocks has a spectacular aura aboutghorrocks has a spectacular aura aboutghorrocks has a spectacular aura about
I cannot view the file, can you use the "Go Advanced" option and use the latex editor to put the equation directly in the post?

Also, please explain what you are modelling and what you know about it. Your description of what you are trying to model sounds strange.
ghorrocks is offline   Reply With Quote

Old   June 20, 2013, 19:10
Default
  #3
mva
New Member
 
Maria
Join Date: Jun 2013
Posts: 3
Rep Power: 4
mva is on a distinguished road
Hi

I have attached the equation as a png file. Is it ok now?

Actually I am trying to derive solutions of the attached diffusion equation for test case i.e., a cube 1x1x1. Initial conditions: (concentration) c=1 at the upper surface,
Boundary conditions:dc/dt=0 at the remaining surfaces.

Thanks
Attached Images
File Type: png equation.png (6.7 KB, 17 views)
mva is offline   Reply With Quote

Old   June 20, 2013, 19:19
Default
  #4
Super Moderator
 
Glenn Horrocks
Join Date: Mar 2009
Location: Sydney, Australia
Posts: 10,646
Rep Power: 84
ghorrocks has a spectacular aura aboutghorrocks has a spectacular aura aboutghorrocks has a spectacular aura about
This is pretty straight forward - a diffusive additional variable with a source term of c^2. Do not use a diffusive transport equation as you are not modelling transport. But non-linear source terms like this sound pretty numerically unstable so you will have to be careful to get it to converge.

Is the density constant? And I do not understand your comment about a point being c=0 far away.

Finally, why is c>1 unphysical? If c is a concentration and therefore bounded to c<=1 then I think your entire approach is wrong - The c^2 source term is obviously an unbounded equation, so you will need to rethink your equation.
ghorrocks is offline   Reply With Quote

Old   June 20, 2013, 20:25
Default
  #5
mva
New Member
 
Maria
Join Date: Jun 2013
Posts: 3
Rep Power: 4
mva is on a distinguished road
Thanks for the reply.

I am not modelling transport but the general form of diffusive-transport equation that is mentioned in the help looks similar to mine if i set D=1, density ρ=1 and S=c^2. Is this right?

I am not saying that c is bounded to be lower than 1;however for the transient problem (duration=1 sec, 10 timesteps), I would expect that the solution at the point (0.5,0.5,0.5) at t=0 is lower than 1.

What do you mean "be careful to get it converge"?What should I do?

I have set the additional variable c as specific without units.Is this ok?

Best
mva is offline   Reply With Quote

Old   June 21, 2013, 03:42
Default
  #6
Super Moderator
 
Glenn Horrocks
Join Date: Mar 2009
Location: Sydney, Australia
Posts: 10,646
Rep Power: 84
ghorrocks has a spectacular aura aboutghorrocks has a spectacular aura aboutghorrocks has a spectacular aura about
Read the documentation carefully about the differences between specific and volumetric additional variables to make sure you have chosen the correct one. I have not looked into this in detail so cannot tell you which option to choose here, you will have to do that.

To get non-linear simulations like this to converge you might need small time steps. Mesh quality might help a little but as your additional variable is just a diffusion equation it will not be a major factor. Also double precision might help.
ghorrocks is offline   Reply With Quote

Reply

Thread Tools
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 On
Pingbacks are On
Refbacks are On


Similar Threads
Thread Thread Starter Forum Replies Last Post
solidification viscosity governed through an additional variable l.te CFX 8 September 13, 2012 19:19
Additional variable Luigi CFX 7 July 23, 2012 09:52
diffusion Term for add. Variable Zaktatir CFX 9 July 16, 2011 09:51
Transport of additional variable bearli CFX 4 July 7, 2010 12:10
Implementing additional equation? Pratap FLUENT 1 December 4, 2004 21:32


All times are GMT -4. The time now is 13:18.