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Old   March 7, 2012, 05:35
Default Fractional steps method
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Can anybody give information about implementing chorin's fractional steps method? I have problems specially about solving poisson equation
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Old   March 8, 2012, 14:44
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Originally Posted by challenger149 View Post
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.
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Old   April 12, 2013, 01:01
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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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Old   April 12, 2013, 03:20
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Originally Posted by o_mars_2010 View Post
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
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Old   April 12, 2013, 03:33
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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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Old   April 12, 2013, 04:17
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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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Old   April 12, 2013, 04:36
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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
Thanks a lot for your help. Do you have any research paper explains how to deal with the outlet ???
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