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 challenger149 March 7, 2012 05:35

Fractional steps method

Can anybody give information about implementing chorin's fractional steps method? I have problems specially about solving poisson equation

 FMDenaro March 8, 2012 14:44

Quote:
 Originally Posted by challenger149 (Post 348083) 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.

 o_mars_2010 April 12, 2013 01:01

Dear FMDenaro
Could you please explain more simply how to modify Div.V* on the boundary, using the normal components of Vn+1??

 FMDenaro April 12, 2013 03:20

Quote:
 Originally Posted by o_mars_2010 (Post 420025) 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

 o_mars_2010 April 12, 2013 03:33

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

 FMDenaro April 12, 2013 04:17

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 April 12, 2013 04:36

Quote:
 Originally Posted by FMDenaro (Post 420069) 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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