Momentum conservation issue in LES?

doctorWho · February 26, 2014, 03:02

Hi,

I am calculating flow around a circular cylinder with LES.
Numerical scheme for time advance is four-step fractional method .
$\frac{\hat{u}_i - {u}_{i}^{n}}{\Delta t} = \frac{1}{2} \left( 3A_{i}^{n} - A_{i}^{n-1} \right) + \frac{1}{2} \left( C_i^{n+1} + C_i^{n} \right) - Grad_i (p^n)$

where A and C are denoted as Adams-Bashforth and Crank-Nicolson schemes.

$\frac{u_i^n-\hat{u}_i}{\Delta t} = Grad_i (p^n)$

$\frac{\partial}{\partial x_i} Grad_i(p^{n+1}) = \frac{1}{\Delta t} \frac{\partial u_i^*}{\partial x_i}$

$\frac{u_i^{n+1}-u_i^*}{\Delta t} = -Grad_i (p^{n+1})$

After solution is statistically converged, I post-processed solutions and calculated momentum balance with momentum equation. in post-process, calculation was made with 1st step.

In post-process, Poisson equation and velocity correction were not made. Is it normal not to have momentum balance with the above process?

Thanks in advance.

FMDenaro · February 26, 2014, 04:47

This is not clear to me... once you computed ui^n+1 from the last step you have all you need ... this field is a filtered velocity, the equation must contain an SGS term, is it included in A?

doctorWho · February 26, 2014, 10:19

Denaro,

Yes, SGS term is included in A.

sbaffini · February 26, 2014, 11:16

How did you exactly quantified the lack of momentum balance?

Consider that the fractional step method does not iterates on the momentum-pressure coupling, hence a second order (in time) inbalance shoul be normal

February 26, 2014, 03:02	Momentum conservation issue in LES?	#1
doctorWho New Member SSSSS Join Date: Jun 2011 Posts: 28 Rep Power: 14	Hi, I am calculating flow around a circular cylinder with LES. Numerical scheme for time advance is four-step fractional method . $\frac{\hat{u}_i - {u}_{i}^{n}}{\Delta t} = \frac{1}{2} \left( 3A_{i}^{n} - A_{i}^{n-1} \right) + \frac{1}{2} \left( C_i^{n+1} + C_i^{n} \right) - Grad_i (p^n)$ where A and C are denoted as Adams-Bashforth and Crank-Nicolson schemes. $\frac{u_i^n-\hat{u}_i}{\Delta t} = Grad_i (p^n)$ $\frac{\partial}{\partial x_i} Grad_i(p^{n+1}) = \frac{1}{\Delta t} \frac{\partial u_i^}{\partial x_i}$ $\frac{u_i^{n+1}-u_i^}{\Delta t} = -Grad_i (p^{n+1})$ After solution is statistically converged, I post-processed solutions and calculated momentum balance with momentum equation. in post-process, calculation was made with 1st step. In post-process, Poisson equation and velocity correction were not made. Is it normal not to have momentum balance with the above process? Thanks in advance.

February 26, 2014, 11:16		#4
sbaffini Senior Member Paolo Lampitella Join Date: Mar 2009 Location: Italy Posts: 2,151 Blog Entries: 29 Rep Power: 39	How did you exactly quantified the lack of momentum balance? Consider that the fractional step method does not iterates on the momentum-pressure coupling, hence a second order (in time) inbalance shoul be normal leflix likes this.

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February 26, 2014, 04:47		#2
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,769 Rep Power: 71	This is not clear to me... once you computed ui^n+1 from the last step you have all you need ... this field is a filtered velocity, the equation must contain an SGS term, is it included in A?

February 26, 2014, 10:19		#3
doctorWho New Member SSSSS Join Date: Jun 2011 Posts: 28 Rep Power: 14	Denaro, Yes, SGS term is included in A.