
[Sponsors] 
June 15, 2012, 08:20 
Coefficients discretized momentum equation

#1 
Senior Member
Join Date: Dec 2011
Location: Madrid, Spain
Posts: 134
Rep Power: 7 
Dear CFDonliners,
I came across a question when trying to solve the momentum equation following Patankar's book (1980) indications. When solving a general transport equation for a certain variable , the discretized form takes the form: , where P,E,W,N,S stand for point, east face, west face, north face and south face, respectively. The coefficients depend on the type of numerical scheme used (central differences, upwind, exponential, power law...). My question: how do we calculate the discretization coefficients for the momentum equations u and v? can we just assume that the momentum equations are another set of convectiondiffusion equations, where the variable are u and v? Then we could just use the same method as before (upwind, power law, ...). Any help will be welcome. Thanks in advance . 

June 18, 2012, 15:07 

#2 
Senior Member
Chris DeGroot
Join Date: Nov 2011
Location: Canada
Posts: 388
Rep Power: 7 
Quote:


June 18, 2012, 17:49 

#3 
Senior Member
Join Date: Dec 2011
Location: Madrid, Spain
Posts: 134
Rep Power: 7 
Hi Chris, I found later in Patankar's book that we could just use any differentiation scheme for the diffusive and convective terms in the momentum equation, as it is done for general convectiondiffusion equations (I also found the coefficients I was looking for in Versteeg&Malalasekera book).
Yes, I will treat the pressure gradient term differently don't worry. I appreciate your reply anyway. Cheers. 

June 19, 2012, 19:16 

#4  
Senior Member
Join Date: Aug 2011
Posts: 251
Rep Power: 8 
Quote:
The momentum equations are EXACTLY convectiondiffusion equations with a source term. In this case the source term is the pressure gradient (dp/dx_i) + cross derivative of velocity (du_j/dx_i). (here d is partial derivative) It can be discretized using the same schemes as the ones used for any scalar transport equation. The scalars here are the componnents of the velocity vector u and v. 

June 20, 2012, 01:33 

#5  
Senior Member
Chris DeGroot
Join Date: Nov 2011
Location: Canada
Posts: 388
Rep Power: 7 
Quote:


Thread Tools  
Display Modes  


Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
solving the momentum equation in UEqn.  callahance  OpenFOAM  2  October 18, 2012 09:38 
Question on the discretization of momentum equation in icoFoam  MPJ  OpenFOAM  3  October 4, 2011 09:44 
Momentum equation of Darcy's law  sambatra  OpenFOAM Running, Solving & CFD  2  April 17, 2009 03:27 
Momentum Equation  Munir Ahmed Khan  FLUENT  0  August 27, 2008 07:57 
Question on momentum equation in VOF or Level Set  Kai Yan  Main CFD Forum  0  January 11, 2008 09:47 