[levinperson]

Hi,

I have a very fundamental question on implementing a LES code. For example, if I want to use a Smagorinsky model or dynamic model, then there is the filtered strain rate (S) in the expressions of the eddy viscosity. As I know, the filtered strain rate is a function of the gradient of the filtered velocity field. My question is how to determine the filtered strain rate when we are writing a LES code? It seems that we can treat the filtered strain rate as a mean constant. But we need to get the filtered velocity field first which is the thing that we are solving by LES...

I appreciate your answer.

Thank you,
Kevin

[FMDenaro]

Once the initial condition is prescribed, you have the filtered velocity field v_bar(x,0), then you can compute the tensor S(x,0). That completes all you need

If you use explicit time integration for the SGS model, you can proceed computing the filtered velocity field at the next time.

If you would try to use an implicit time integration for the SGS term, you get into the problem that the resulting system is not linear. Some linearization can be used.

[levinperson]

Originally Posted by FMDenaro

Once the initial condition is prescribed, you have the filtered velocity field v_bar(x,0), then you can compute the tensor S(x,0). That completes all you need

If you use explicit time integration for the SGS model, you can proceed computing the filtered velocity field at the next time.

If you would try to use an implicit time integration for the SGS term, you get into the problem that the resulting system is not linear. Some linearization can be used.

Hi Filippo,

Thank you for your reply. I'm currently using an explicit method which is simpler to implement. Based on your explanation, we are using the mean filtered strain rate obtained from the filtered velocity field at time level n to solve the filtered velocity V_bar at the time level n+1. Is this correct?

Kevin

[FMDenaro]

Yes.

However, also explicit multi-level scheme can be used, based on time n, n-1, ...

[levinperson]

Originally Posted by FMDenaro

Yes.

However, also explicit multi-level scheme can be used, based on time n, n-1, ...

OK, I see. Can I ask you another question? We are going to solve a 1D Burgers equation with viscous term by LES. The grid number is 200 for example. The filter width 'Delta' I choose is twice of the grid spacing h. The initial condition of the velocity field has been prescribed. If I want to start my simulation, should I filter the initial velocity field first with the filter width 'Delta=2*h', or just apply the initial condition directly to solve the velocity at time level t=1*dt? The reason I ask this question is that I feel that since the filter width is only twice of the grid spacing, filtering process like this doesn't make too much sense. If we have a grid spacing small enough to resolve the velocity field, then we should filter the velocity first before running the LES code.

Another thing is that I'm using a MacCormack method (2nd order in time and space) to solve this viscous 1D Burgers equation. To perform a DNS simulation, the time step size has to be very small to get accurate results... Could you give me some suggestions on some other schemes with a minimum 2nd order accuracy? Thank you so much!

Kevin

[FMDenaro]

The assumption that Delta = 2*h is quite arbitrary.... if you want to compute an initial filtered field from an initial pointwise velocity field you should use the same shape and width of the filter using during the simulation. But if you are working with implicit-based filtering, the shape and width of the filter is implicitly defined by the numerical scheme you adopt.

I suggest to start from a prescribed initial state, assuming it already represents the intial filtered field. You will run the simulation for several time step and thereafter the initial solution will become less relevant.

If you want, give a look to my old paper about Burgers

https://www.researchgate.net/publica...dy_simulations