
[Sponsors] 
May 3, 2013, 06:07 
discretisation

#1 
New Member
ramin abedifard
Join Date: Jul 2012
Posts: 12
Rep Power: 5 
Hello
I want to discretise one term of non fourier heat transfer equation with volume control method. I try to do it, but i cant. this term is: d2(cp u T)/(dt dx) that we have cp(T),u(x,y,t),T(x,y,t) T:temperate t:time thank you Last edited by ramin; May 3, 2013 at 16:32. 

May 3, 2013, 08:34 

#2 
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 2,007
Rep Power: 27 
I have some doubt about your symbolism, you are referring to as a first time derivative or a second mixed x,t derivative....?


May 3, 2013, 16:40 

#3 
New Member
ramin abedifard
Join Date: Jul 2012
Posts: 12
Rep Power: 5 

May 3, 2013, 17:52 

#4 
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 2,007
Rep Power: 27 

May 4, 2013, 03:16 

#5 
New Member
ramin abedifard
Join Date: Jul 2012
Posts: 12
Rep Power: 5 

May 4, 2013, 04:57 

#6 
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 2,007
Rep Power: 27 

May 4, 2013, 07:13 

#7 
New Member
ramin abedifard
Join Date: Jul 2012
Posts: 12
Rep Power: 5 
It is a hyperbolic heat transfer equation. It should be discretised base on versteegَ s book(An introduction to computational fluid dynamics) and with volume control method.


May 4, 2013, 13:46 

#8 
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 2,007
Rep Power: 27 
Your question is not clear to me... to the best of my knowledge, a term like d2T/dxdt never appears in the original heat equation....
hybrid timespace derivatives usually appears when you use some timeintegration method of the class of the LaxWendroff. But in such cases, the original equation is substituted into the derivative. 

May 4, 2013, 18:26 

#9  
New Member
ramin abedifard
Join Date: Jul 2012
Posts: 12
Rep Power: 5 
Quote:
This term is very small, since it has a very small fixed coefficient. This coefficient shows the speed of heat propagation is not infinite. 

May 5, 2013, 04:13 

#10  
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 2,007
Rep Power: 27 
Quote:
Again, the real problem is not in the discretization of a single term (is quite simple to do on a timespace grid) but care in the discretization of the model equation is required. You said it is hyperbolic, therefore the discretization of the whole model must be stable and accurate, but if the equation is also nonlinear other requirements can be necessary. 

May 5, 2013, 05:44 

#11  
New Member
ramin abedifard
Join Date: Jul 2012
Posts: 12
Rep Power: 5 
Quote:


Thread Tools  
Display Modes  


Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
8th order polynomial function(VOF smoothening) + ENO discretisation  bharat.cmeri  FLUENT  1  July 4, 2012 11:51 
Transient term discretisation scheme  Batis  CFX  2  August 23, 2010 20:17 
Second Order Discretisation with Porous Media  giogio  FLUENT  1  March 21, 2008 13:29 
Discretisation scheme in CFX1st or 2nd order?  Pete  CFX  10  January 12, 2005 13:48 
compressive discretisation scheme  Jennifer Haque  CFX  7  July 29, 2004 05:00 