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Boundary condition: intermediate velocity for fractional time step method

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Old   June 19, 2015, 18:37
Default Boundary condition: intermediate velocity for fractional time step method
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Hi!
How to calculate u*=u_n+1 for the intermediate velocity u*
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Old   June 20, 2015, 03:47
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Hi!
How to calculate u*=u_n+1 for the intermediate velocity u*

are you talking about the intermediate BC.s in the fractional time step method? The literature is full of paper about this issue, starting from the hystorical paper of Kim & Moin on JCP you can find many many studies and proposals.

However, u_n+1 is the physical BC you have to know, a zero-order approximation simply set it as u*.
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Old   June 20, 2015, 07:25
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Thank u for the reply.
yes for fractional time step method
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Old   June 20, 2015, 14:24
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I use FSM with free pressure
boundary :

1)n.u*=n.u_n+1
u*=u_n+1
=> u*=u_n+dt*u_t
=u_n+dt*(-u*grad_u+(1/rho)*(mu*laplace(u)+grad_pression+F) is correct??
(depent to density rho)

2) t.u*=t.(u_n+1+(dt*grad_Phi)

3) for pressure:

laplace(phi)=(rho/dt)*div u^*
boundary n.grad_phi=0

4) and to calculate u_n+1
u_n+1=u*-(dt/rho)*grad_phi
No boundary conditions, ie I compute the velocity for interior and boundary points.

PS: I am beginner in CFD
I need your help
Thank you
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Old   June 20, 2015, 18:27
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I think your process need a careful revision...


1) Are you using a second order implicit time integration in the momentum equation?

2) The pressure equation is nothing else but the continuity equation in which the Hodge decomposition is substituded.

3) You need to take care of the product Div Grad, I suggest not to write it as Laplacian for a correct setting of the Neuman BC.s

4) What books/papers are you studying for the FTS method?
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Old   June 20, 2015, 18:48
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for time discretisation I use Adams Bashforth and Crank Nicolson scheme.

[1] Application of a Fractional-Step Method to Incompressible Navier-Stokes Equations
J. KIM AND P. MOIN
[2] David L. Brown, Ricardo Cortez,y and Michael L. Minionz Accurate Projection Methods for the Incompressible Navier–Stokes Equations
[3]J.L. Guermond, P. Minev c, Jie Shen An overview of projection methods for incompressible flows

and other paper for spatial discretisation (Radial basis function).
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Old   June 21, 2015, 03:21
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Originally Posted by Rime View Post
for time discretisation I use Adams Bashforth and Crank Nicolson scheme.

[1] Application of a Fractional-Step Method to Incompressible Navier-Stokes Equations
J. KIM AND P. MOIN
[2] David L. Brown, Ricardo Cortez,y and Michael L. Minionz Accurate Projection Methods for the Incompressible Navier–Stokes Equations
[3]J.L. Guermond, P. Minev c, Jie Shen An overview of projection methods for incompressible flows

and other paper for spatial discretisation (Radial basis function).

Ok, therefore you solve the implicit scheme for v* using the BC.s v* = v_n+1 + dt Grad phi_n, right?

Then you solve the elliptic equation Dic Grad phi_n+1 = Div q, wherein q is the source term.

What's wrong with your results?
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Old   June 21, 2015, 07:01
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Thank you for the reply.

my result diverge and when I use steady boundary I get a false solution.
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Old   June 21, 2015, 07:10
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Thank you for the reply.

my result diverge and when I use steady boundary I get a false solution.

check if you satisfy the continuity equation in each node just after the first time step.
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Old   June 21, 2015, 07:16
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I get div u around 0.04
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Old   June 21, 2015, 07:29
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I get div u around 0.04

you have some bug in the code, I think in setting the BC.s for the pressure equation.
Are you setting:

d phi/dn = (1/dt) ( v*-v_n+1).n

in the Poisson equation?
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Old   June 21, 2015, 07:42
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Quote:
Originally Posted by Rime View Post
boundary :

u*=u_n+dt*u_t
=u_n+dt*(-u*grad_u+(1/rho)*(mu*laplace(u)+grad_pression+F) is correct??

n.u*=n.(u_n+1+(dt*grad_Phi)

for pressure:
boundary n.grad_phi=0
So I use n.grad_phi=0
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Old   June 21, 2015, 08:31
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So I use n.grad_phi=0
have you modified the source term in a consequent way?
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Old   June 21, 2015, 08:36
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have you modified the source term in a consequent way?
sorry, I don't understand the question
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Old   June 21, 2015, 08:43
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sorry, I don't understand the question
the source term in the Poisson equation has been modified in a way congruent to the setting d phi/dn=0? How do you compute it?
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Old   June 21, 2015, 09:19
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the source term in the Poisson equation has been modified in a way congruent to the setting d phi/dn=0? How do you compute it?
div grad_phi = Div u^*
n.u^* = n.u_n+1 + n.grad_phi
so
n.grad_phi= n.(u^* - u_n+1^*)

I look that in my code I consider that the velocity in the boundary equal to zero (therefore that is false)
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Old   June 21, 2015, 11:58
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Originally Posted by Rime View Post
div grad_phi = Div u^*
n.u^* = n.u_n+1 + n.grad_phi
so
n.grad_phi= n.(u^* - u_n+1^*)

I look that in my code I consider that the velocity in the boundary equal to zero (therefore that is false)

As you see, if you set in n.u^* = n.u_n+1 + n.grad_phi the BC.s :

n.grad_phi=0 ,

you MUST set also

n.u^* = n.u_n+1

therfore in computing the source term

Div u^*

you have to use the physical BC.s n.u_n+1.
One you have fulfilled such constraints, you have the compatibility condition satisfied and the Poisson equation will converge.
Finally, if you use a staggered secondo order discretization you should have the continuity equation satisfied up to machine precision
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Old   June 21, 2015, 12:34
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Originally Posted by FMDenaro View Post

n.u^* = n.u_n+1

therfore in computing the source term
Div u^*
you have to use the physical BC.s n.u_n+1.
Thank you for your time, very useful.

n.u^* = n.u_n+1 <=> n.u^* = n.u_bc (bc=boundary condition)
because I can't see the difference between u_n+1 and steady u_bc
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Old   June 21, 2015, 12:37
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Thank you for your time, very useful.

n.u^* = n.u_n+1 <=> n.u^* = n.u_bc (bc=boundary condition)
because I can't see the difference between u_n+1 and steady u_bc

well, that's ok if the BC.s are steady. It must work
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Old   June 21, 2015, 12:44
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well, that's ok if the BC.s are steady. It must work
Thank you, I will try again.
I hope it works
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