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

How to define fluxes for two dimensional convection-diffusion equation?

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

Reply
 
LinkBack Thread Tools Search this Thread Display Modes
Old   September 9, 2015, 12:40
Default
  #21
New Member
 
Tanmay Agrawal
Join Date: May 2015
Location: Taiwan
Posts: 29
Rep Power: 11
tanmayagrawal7 is on a distinguished road
Send a message via Skype™ to tanmayagrawal7
Quote:
Originally Posted by FMDenaro View Post
you are working with u and v constant and known? In this case, the solution is a simple linear wave propagating along the path-line, the grid-refinement should move dynamically
Yes. U and V equals one. I just want to check my local mesh refinement algorithm and want to make sure that it is giving better result than when there is no refinement. Then later on, I would change it to be a dynamic mesh once the procedure turns out to be right.
tanmayagrawal7 is offline   Reply With Quote

Old   September 9, 2015, 12:49
Default
  #22
Senior Member
 
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,892
Rep Power: 73
FMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura about
Quote:
Originally Posted by tanmayagrawal7 View Post
Yes. U and V equals one. I just want to check my local mesh refinement algorithm and want to make sure that it is giving better result than when there is no refinement. Then later on, I would change it to be a dynamic mesh once the procedure turns out to be right.

local steady refinement can not help improving this kind of solution
FMDenaro is online now   Reply With Quote

Old   September 9, 2015, 12:55
Default
  #23
New Member
 
Tanmay Agrawal
Join Date: May 2015
Location: Taiwan
Posts: 29
Rep Power: 11
tanmayagrawal7 is on a distinguished road
Send a message via Skype™ to tanmayagrawal7
Quote:
Originally Posted by FMDenaro View Post
local steady refinement can not help improving this kind of solution
Why is that so professor? Say, I am validating my results along the centerline where there is a sudden jump of solution from 0 to 1. With local mesh refinement here along the center, should not I be able to manage to get a better solution?
tanmayagrawal7 is offline   Reply With Quote

Old   September 9, 2015, 12:58
Default
  #24
Senior Member
 
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,892
Rep Power: 73
FMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura about
Quote:
Originally Posted by tanmayagrawal7 View Post
Why is that so professor? Say, I am validating my results along the centerline where there is a sudden jump of solution from 0 to 1. With local mesh refinement here along the center, should not I be able to manage to get a better solution?

this jump will rapidly move far from the refined region
FMDenaro is online now   Reply With Quote

Old   September 9, 2015, 13:01
Default
  #25
New Member
 
Tanmay Agrawal
Join Date: May 2015
Location: Taiwan
Posts: 29
Rep Power: 11
tanmayagrawal7 is on a distinguished road
Send a message via Skype™ to tanmayagrawal7
Quote:
Originally Posted by FMDenaro View Post
this jump will rapidly move far from the refined region
In my particular case with the boundary conditions that I am using, this jump remains in steady state. You can imagine a square with top and left sides on 1 and right and bottom sides on 0 initial value. At steady state, the center point of square is where the jump happens. You are right that in transient case, this will keep moving like a wave.
tanmayagrawal7 is offline   Reply With Quote

Old   September 9, 2015, 13:08
Default
  #26
Senior Member
 
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,892
Rep Power: 73
FMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura about
your BC.s cannot be prescribed on all the edges of the box but only at left and bottom .....
FMDenaro is online now   Reply With Quote

Old   September 9, 2015, 13:11
Default
  #27
New Member
 
Tanmay Agrawal
Join Date: May 2015
Location: Taiwan
Posts: 29
Rep Power: 11
tanmayagrawal7 is on a distinguished road
Send a message via Skype™ to tanmayagrawal7
Quote:
Originally Posted by FMDenaro View Post
your BC.s cannot be prescribed on all the edges of the box but only at left and bottom .....
Why is that so professor? I remember I have earlier solved 1D inviscid Burgers equation in which I had BC on both of the ends of domain. And how would I deal with the top and right two boundaries if this is the case? Periodic BC?
tanmayagrawal7 is offline   Reply With Quote

Old   September 9, 2015, 13:18
Default
  #28
Senior Member
 
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,892
Rep Power: 73
FMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura about
Quote:
Originally Posted by tanmayagrawal7 View Post
Why is that so professor? I remember I have earlier solved 1D inviscid Burgers equation in which I had BC on both of the ends of domain. And how would I deal with the top and right two boundaries if this is the case? Periodic BC?
that's wrong, the 1D Burgers equation requires only one BC. to be well posed.
FMDenaro is online now   Reply With Quote

Old   September 9, 2015, 13:21
Default
  #29
New Member
 
Tanmay Agrawal
Join Date: May 2015
Location: Taiwan
Posts: 29
Rep Power: 11
tanmayagrawal7 is on a distinguished road
Send a message via Skype™ to tanmayagrawal7
Quote:
Originally Posted by FMDenaro View Post
that's wrong, the 1D Burgers equation requires only one BC. to be well posed.
For that case actually, I had used the initial condition and boundary conditions from the PhD thesis of Marsha Berger(who proposed adaptive mesh refinement for hyperbolic PDE that I want to use). But even with 2 BC, it got solved well.
tanmayagrawal7 is offline   Reply With Quote

Old   September 9, 2015, 13:31
Default
  #30
Senior Member
 
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,892
Rep Power: 73
FMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura about
Quote:
Originally Posted by tanmayagrawal7 View Post
For that case actually, I had used the initial condition and boundary conditions from the PhD thesis of Marsha Berger(who proposed adaptive mesh refinement for hyperbolic PDE that I want to use). But even with 2 BC, it got solved well.
I don't know such thesis but I know that the Cauchy problem requires only one BC to be well posed.
I strongly suggest to better study the character of the equations and the required boundary conditions
FMDenaro is online now   Reply With Quote

Old   September 9, 2015, 22:19
Default
  #31
New Member
 
Tanmay Agrawal
Join Date: May 2015
Location: Taiwan
Posts: 29
Rep Power: 11
tanmayagrawal7 is on a distinguished road
Send a message via Skype™ to tanmayagrawal7
Quote:
Originally Posted by FMDenaro View Post
I don't know such thesis but I know that the Cauchy problem requires only one BC to be well posed.
I strongly suggest to better study the character of the equations and the required boundary conditions
Thanks professor! So in my two dimensional case, what kind of BC will I need on the other two edges?
tanmayagrawal7 is offline   Reply With Quote

Old   September 10, 2015, 04:41
Default
  #32
Senior Member
 
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,892
Rep Power: 73
FMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura about
Quote:
Originally Posted by tanmayagrawal7 View Post
Thanks professor! So in my two dimensional case, what kind of BC will I need on the other two edges?

you can prescribe the value of T only on the edges where the flow enters (left and bottom), no BC.s have to be prescribed when the flow leaves the domain
FMDenaro is online now   Reply With Quote

Reply

Tags
finite difference, finite volume, math, mesh, pde

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
Model crashes while solving advection diffusion equation cooljd Main CFD Forum 3 August 23, 2012 11:40
Spectral Element DG and the Convection Diffusion Equation sspatelccny Main CFD Forum 0 June 30, 2012 18:35
error message cuteapathy CFX 14 March 20, 2012 07:45
Define an equation for the inlet velocity profile Alshroof CFX 3 January 9, 2007 20:34
Free surface boudary conditions with SOLA-VOF Fan Main CFD Forum 10 September 9, 2006 13:24


All times are GMT -4. The time now is 23:04.