Some questions and concerns on LES

selig5576 · December 4, 2017, 13:38

I am interested in taking on the feat of implementing a LES model for my finite volume method. I am of the understanding we can write the filtered incompressible NS (using the Boussinesq approximation) as

Where the modified pressure is

$\bar{P} = p + \frac{1}{3} \tau_{kk},$

where $\tau_{kk}$ is the trace component, i.e. $\tau_{kk} = \frac{\partial \bar{U}_{k}}{\partial x_{k}}$ .

For simplicity I want to start with a simple dynamic model, such as the Smagorinsky SGS model. According to literature I am currently using second order central differencing as upwind schemes perform quite poorly in LES. In terms of explicit filtering, what I am confused about is when to apply the filter. Naively, I would apply the filter after each timestep to $\mathbf{u}^{n+1}$ . But doing the algebra of applying the filter, it seems that applying it to $\mathbf{u}^{n+1}$ isnt satisfactory as applying the explicit filter to the nonlinear advection term. The filter I am interested in is

$\bar{\mathbf{u}} = - \frac{1}{32} \mathbf{u}_{i-3} + \frac{9}{32} \mathbf{u}_{i-1} + \frac{1}{2} \mathbf{u}_{i} + \frac{9}{32} \mathbf{u}_{i+1} - \frac{1}{32} \mathbf{u}_{i+3}$

This filter was proposed by J. Gullbrand. Also, for initial testing of the addition of LES to my FVM solver, is the cubic lid driven cavity acceptable? Given I am in the early stages of using LES, would maybe implicit filtering be more appropriate?

FMDenaro · December 4, 2017, 14:35

1) I suggest to start your experience in the LES field implementing first the implicit filtering approach. However, the explicit filtering is applied on the convective flux.
2) Use the convective form of the non linear term instead of the quasi-linear form.
3) The lid driven cavity is not the correct test case to assess the performance of your LES code

selig5576 · December 4, 2017, 14:58

Thank you for the replies. I think the implicit filtering approach is the right one for me given my limited experience. With regards to implicit LES filtering, I am of the understanding the filter is not explicitly implemented, but rather it is based on your grid resolution and numerical methods. Is this the correct view to have? In implementation, it feels more like RANS then LES in terms of the form of the momentum equation. Thanks!

FMDenaro · December 4, 2017, 15:02

Quote:

Originally Posted by selig5576

Thank you for the replies. I think the implicit filtering approach is the right one for me given my limited experience. With regards to implicit LES filtering, I am of the understanding the filter is not explicitly implemented, but rather it is based on your grid resolution and numerical methods. Is this the correct view to have? In implementation, it feels more like RANS then LES in terms of the form of the momentum equation. Thanks!

You are correct.

selig5576 · December 6, 2017, 13:47

For a inlet condition that satisfies mass conservation, are there papers you could recommend that discuss turbulent inlet BCs? I am trying to avoid just adding noise to my laminar inlet as that will yield incorrect statistics. Thank you again.

FMDenaro · December 6, 2017, 13:56

See Section 10.3 in the book of Sagaut and the cited references

December 4, 2017, 13:38	Some questions and concerns on LES	#1
selig5576 Senior Member Selig Join Date: Jul 2016 Posts: 213 Rep Power: 10	I am interested in taking on the feat of implementing a LES model for my finite volume method. I am of the understanding we can write the filtered incompressible NS (using the Boussinesq approximation) as Where the modified pressure is $\bar{P} = p + \frac{1}{3} \tau_{kk},$ where $\tau_{kk}$ is the trace component, i.e. $\tau_{kk} = \frac{\partial \bar{U}_{k}}{\partial x_{k}}$ . For simplicity I want to start with a simple dynamic model, such as the Smagorinsky SGS model. According to literature I am currently using second order central differencing as upwind schemes perform quite poorly in LES. In terms of explicit filtering, what I am confused about is when to apply the filter. Naively, I would apply the filter after each timestep to $\mathbf{u}^{n+1}$ . But doing the algebra of applying the filter, it seems that applying it to $\mathbf{u}^{n+1}$ isnt satisfactory as applying the explicit filter to the nonlinear advection term. The filter I am interested in is $\bar{\mathbf{u}} = - \frac{1}{32} \mathbf{u}_{i-3} + \frac{9}{32} \mathbf{u}_{i-1} + \frac{1}{2} \mathbf{u}_{i} + \frac{9}{32} \mathbf{u}_{i+1} - \frac{1}{32} \mathbf{u}_{i+3}$ This filter was proposed by J. Gullbrand. Also, for initial testing of the addition of LES to my FVM solver, is the cubic lid driven cavity acceptable? Given I am in the early stages of using LES, would maybe implicit filtering be more appropriate?

December 4, 2017, 14:58	Starting in LES	#3
selig5576 Senior Member Selig Join Date: Jul 2016 Posts: 213 Rep Power: 10	Thank you for the replies. I think the implicit filtering approach is the right one for me given my limited experience. With regards to implicit LES filtering, I am of the understanding the filter is not explicitly implemented, but rather it is based on your grid resolution and numerical methods. Is this the correct view to have? In implementation, it feels more like RANS then LES in terms of the form of the momentum equation. Thanks!

December 6, 2017, 13:47	Some progress	#5
selig5576 Senior Member Selig Join Date: Jul 2016 Posts: 213 Rep Power: 10	For a inlet condition that satisfies mass conservation, are there papers you could recommend that discuss turbulent inlet BCs? I am trying to avoid just adding noise to my laminar inlet as that will yield incorrect statistics. Thank you again.

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December 4, 2017, 14:35		#2
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,768 Rep Power: 71	1) I suggest to start your experience in the LES field implementing first the implicit filtering approach. However, the explicit filtering is applied on the convective flux. 2) Use the convective form of the non linear term instead of the quasi-linear form. 3) The lid driven cavity is not the correct test case to assess the performance of your LES code

December 6, 2017, 13:56		#6
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,768 Rep Power: 71	See Section 10.3 in the book of Sagaut and the cited references