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March 7, 2012, 04:35 |
Fractional steps method
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#1 |
New Member
Mohammad Kazem Sharifian
Join Date: May 2011
Posts: 7
Rep Power: 14 |
Can anybody give information about implementing chorin's fractional steps method? I have problems specially about solving poisson equation
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March 8, 2012, 13:44 |
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#2 | |
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,764
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Quote:
V* = Vn+1 + Grad (phi) Taking divergence of both sides you get Div (Grad (phi)) = Div V* with the BCs: d phi/dn = n . (V* - Vn+1) The latter condition says that you hav to modify Div V* on the boundary using the normal component of Vn+1 and use homogeneous Neumann BC d phi/dn=0. This way the compatibility equation is verified and you get a unique solution apart a constant value. |
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April 12, 2013, 01:01 |
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#3 |
Member
Osman
Join Date: Oct 2012
Location: Japan
Posts: 53
Rep Power: 13 |
Dear FMDenaro
Could you please explain more simply how to modify Div.V* on the boundary, using the normal components of Vn+1?? |
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April 12, 2013, 03:20 |
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#4 | |
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,764
Rep Power: 71 |
Quote:
Div (Grad (phi)) = Div V* (1) with the BCs: d phi/dn = n . (V* - Vn+1) -> n . V* = d phi/dn - n . Vn+1 then substitute in RHS of (1) and simplify the terms |
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April 12, 2013, 03:33 |
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#5 |
Member
Osman
Join Date: Oct 2012
Location: Japan
Posts: 53
Rep Power: 13 |
But how do we know the value of Vn+1
if we have a free stream inlet velocity in the inlet, So, Vn+1 will be known in the inlet. what about the other boundaries i.e walls and outlet. Vn+1 is not known at these boundaries ??? Sorry if my understanding is wrong |
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April 12, 2013, 04:17 |
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#6 |
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,764
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on a wall n.Vn+1 must be prescribed ... some difficulties can appear for an outlet where you have to prescribe some condition derived by physical assumption
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April 12, 2013, 04:36 |
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#7 |
Member
Osman
Join Date: Oct 2012
Location: Japan
Posts: 53
Rep Power: 13 |
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