
[Sponsors] 
May 2, 2013, 12:13 
Upwind scheme (in a cell with zero velocity)

#1 
New Member
Molly Tom
Join Date: May 2013
Posts: 3
Rep Power: 6 
I am somewhat new to CFD and am wondering how the first order upwind scheme would be applied to a cell with a zero velocity. It is my understanding that, in the upwind scheme, the sign of the cell velocity is used to determine which cell velocities are applied at the cell faces. But what happens when the cell velocity is zero (how is the upwind direction determined)? This is probably not important in a large region of zero velocity cells, but I'm thinking about a zero velocity cell that is adjacent to a nonzero velocity cell.


May 2, 2013, 12:19 

#2  
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 3,339
Rep Power: 37 
Quote:
where you have zero velocity there is no convective flux contributing to the balance.... 

May 2, 2013, 13:17 

#3 
New Member
Molly Tom
Join Date: May 2013
Posts: 3
Rep Power: 6 
But wouldn't it matter in a case like this?
 i1i i+1 u(i1)=1 u(i)=0 u(i+1)=0   u(i1/2)=???u(i+1/2)=0 So, for cell (i), shouldn't the first order upwind scheme assign a value of u(i1/2)=1? But how would the upwind scheme determine this, because the velocity at cell (i) is zero? 

May 2, 2013, 13:47 

#4 
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 3,339
Rep Power: 37 
 In FD scheme, you evaluate u*du/dx which is zero at node i as u(i)=0.
 In FV scheme you need to evaluate the flux difference f(i+1/2)  f(i1/2). Now you can evaluate the velocity at the interface by means of linear interpolation: u(i1/2) = 0.5*(u(i)+u(i1)); u(i+1/2) = 0.5*(u(i)+u(i+1)) Then the sign will be the direction for evaluating the upwinded flux. Note that your example is a discontinuity travelling 

May 6, 2013, 14:04 

#5 
New Member
Molly Tom
Join Date: May 2013
Posts: 3
Rep Power: 6 
Yes. Thank you very much, I think I understand now. For computing the upwind flux direction, the velocity at the cell interface is computed by averaging the velocities at the cell centers that bound the interface. But, for the firstorder upwind scheme (once the upwind direction has been determined), the interface fluxes are evaluated using the appropriate cell center velocity.


Thread Tools  
Display Modes  


Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Difficulty in calculating angular velocity of Savonius turbine simulation  alfaruk  CFX  14  March 17, 2017 07:08 
Are backward scheme and the upwind scheme the same thing in FDM?  lnk  Main CFD Forum  1  August 30, 2012 02:38 
Velocity from an upwind cell  vitke  OpenFOAM Running, Solving & CFD  0  September 3, 2007 06:15 
Trimmed cell and embedded refinement mesh conversion issues  michele  OpenFOAM Other Meshers: ICEM, Star, Ansys, Pointwise, GridPro, Ansa, ...  2  July 15, 2005 04:15 
DPM velocity at cell face  Szabolcs Varga  FLUENT  1  September 16, 2004 07:30 