Fractional steps method

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 March 7, 2012, 05:35 Fractional steps method #1 New Member   Mohammad Kazem Sharifian Join Date: May 2011 Posts: 7 Rep Power: 8 Can anybody give information about implementing chorin's fractional steps method? I have problems specially about solving poisson equation

March 8, 2012, 14:44
#2
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Filippo Maria Denaro
Join Date: Jul 2010
Posts: 3,751
Rep Power: 41
Quote:
 Originally Posted by challenger149 Can anybody give information about implementing chorin's fractional steps method? I have problems specially about solving poisson equation
once computed the intermediate non-solenoidal field you use the Hodge decomposition

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.

 April 12, 2013, 01:01 #3 Member   Osman Join Date: Oct 2012 Location: Japan Posts: 51 Rep Power: 7 Dear FMDenaro Could you please explain more simply how to modify Div.V* on the boundary, using the normal components of Vn+1??

April 12, 2013, 03:20
#4
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Filippo Maria Denaro
Join Date: Jul 2010
Posts: 3,751
Rep Power: 41
Quote:
 Originally Posted by o_mars_2010 Dear FMDenaro Could you please explain more simply how to modify Div.V* on the boundary, using the normal components of Vn+1??
The equation is:

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

 April 12, 2013, 03:33 #5 Member   Osman Join Date: Oct 2012 Location: Japan Posts: 51 Rep Power: 7 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

 April 12, 2013, 04:17 #6 Senior Member   Filippo Maria Denaro Join Date: Jul 2010 Posts: 3,751 Rep Power: 41 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 o_mars_2010 likes this.

April 12, 2013, 04:36
#7
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Osman
Join Date: Oct 2012
Location: Japan
Posts: 51
Rep Power: 7
Quote:
 Originally Posted by FMDenaro 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
Thanks a lot for your help. Do you have any research paper explains how to deal with the outlet ???

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