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July 15, 2005, 23:39 
Help: diffusive flux BC at wall

#1 
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hi,
i've written a nonstaggered FVM NS solver based on fractional step in cartesian grid. i've used the BC based on peric's book which states that du/dx & dv/dy =0 at the wall, hence diffusive flux at wall=0. my diffusive flux are also handled implicitly now i'm modifying to structured grids. there's no transformation involved and i'm evaluating the fluxes in the physical face. hence, i'm still using u & v in x,y components Now along the wall boundary, du(n)/dn=0 as before. however, my cell centered vel are still in x,y components. how do i make use of du(n)/dn=0 or do i just neglect this condition? Thanks alot! 

July 16, 2005, 01:15 
Re: Help: diffusive flux BC at wall

#2 
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A non moving solid wall BC in 2D is simply u=v=0 not their gradients, check your reference, the gradients equal zero at an exit BC


July 16, 2005, 13:26 
Re: Help: diffusive flux BC at wall

#3 
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Why do you think du(n)/dn should be zero?? Maybe on a separation point but surely not in general.
Doesn't Peric's book give you any information on boundary conditions on curvilinear walls? Maybe you should look beyond Peric's book, which is a little dated anyway. 

July 16, 2005, 17:19 
Re: Help: diffusive flux BC at wall

#4 
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> I've written a nonstaggered FVM NS solver based on fractional step
: in cartesian grid. i've used the BC based on peric's book which states : that du/dx & dv/dy =0 at the wall, From continuity assuming a constant density. > hence diffusive flux at wall=0. No. The gradient of the tangential velocity components is most certainly not zero except for a stationary flow. You need either some loglaw type expression for y+ > 20, to extrapolate the internal velocity gradient for y+ < 1 or something a bit more challenging in between. 

July 16, 2005, 20:34 
Re: Help: diffusive flux BC at wall

#5 
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well, that is strange. Quoted from peric's book (summarised):
at wall, no slip condition applies ie fluid vel = wall vel. another condition can be directly imposed in a FVM; normal viscous stress is zero at a wall. this follows from continuity eqn e.g for a wall at y=0 (bottom), (du/dx)wall = 0 therefore (dv/dy)wall = 0 and tau(yy) = 0 hence diffusive flux at bottom wall = 0. similar for left/right wall, (du/dx)wall =0 so diff. flux tau(xx)=0. for complex geometry, (dv(n)/dn)wall = 0 hence tau(nn) = 0. can somebody verify this? btw, some BC are given in this message. is this correct? http://www.cfdonline.com/Forum/main...cgi?read=14551 thanks alot! 

July 16, 2005, 20:38 
Re: Help: diffusive flux BC at wall

#6 
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also see this message: http://www.cfdonline.com/Forum/main...cgi?read=13665
which states that: "In incompressible viscous flows, velocity divergence condition demands that the wall normal component of velocity has zero gradient along the wall normal" thanks 

July 16, 2005, 23:56 
Re: Help: diffusive flux BC at wall

#7 
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It is always a good idea to check Peric web site for latest updates ftp://ftp.springer.de/pub/technik/peric/newprint/
If you apply the continuity equation at the wall, then in the 2D case du/dx(wall)+ dv/dy(wall) = 0 Why are you taking du/dx(wall) equal to zero, under what conditions this is valid. Explain or send an email to Peric and put his reply on this forum 

July 17, 2005, 11:24 
Re: Help: diffusive flux BC at wall

#8 
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> for complex geometry, (dv(n)/dn)wall = 0 hence tau(nn) = 0.
: can somebody verify this? As Ahmed has said, it follows from continuity (constant density) and recognizing that the tangential velocity components are zero at the wall and hence so are their gradients in directions within the plane of the wall. It does not follow that the gradients of the tangential velocity components in the direction normal to the surface are zero. This is, of course, the boundary layer. I think confusion has arisen by using the word flux without stating the flux of what and we have not all been considering the same components. You must apply all required boundary conditions. If the wall is at an angle to the Cartesian axes then you need to consider what the imposition of boundary conditions expressed in wall coordinates means to the velocity components you are using as solution variables. 

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