[lucamirtanini]

Hi all,
the software that I use (FDS) uses a default Deardorff subgrid model. Looking at this explanation of the Deardorff model I have seen this (see attached figure) strange definition of subgrid kinetic energy, which implies the adoption of a test filter. I look at the paper of Deardorff and I didn't find the same definition of subgrid kinetic energy. I was sure that the the adoption of a test filter was a prerogative of the dynamic smagorinsky model. Can you explain me why they use this definition?? Are they using the test filter also in the Deardorff subgrid model?



[1] J.W. Deardorff. Stratocumulus-capped mixed layers derived from a three-dimensional model. Boundary-Layer Meteorol., 18:495–527, 1980. 10, 29, 30

[FMDenaro]

Originally Posted by lucamirtanini

Hi all,
the software that I use (FDS) uses a default Deardorff subgrid model. Looking at this explanation of the Deardorff model I have seen this (see attached figure) strange definition of subgrid kinetic energy, which implies the adoption of a test filter. I look at the paper of Deardorff and I didn't find the same definition of subgrid kinetic energy. I was sure that the the adoption of a test filter was a prerogative of the dynamic smagorinsky model. Can you explain me why they use this definition?? Are they using the test filter also in the Deardorff subgrid model?



[1] J.W. Deardorff. Stratocumulus-capped mixed layers derived from a three-dimensional model. Boundary-Layer Meteorol., 18:495–527, 1980. 10, 29, 30

It seems a scale-similarity like assumption to evaluate the term (u')_bar. The u_bar filter and (u_bar)^ should be considered at level of the same filter width, from a numerical point of view. Even if it is stated that the "test filter" is at a width 2*Delta, the numerical procedure of averaging over adjacent cells would produce the same numerical filter width of the primary filter (which is implictly defined by the discretization).

The text stated that is a variation of the method, in the original Deardoff's procedure the k equation is solved.

[lucamirtanini]

Originally Posted by FMDenaro

It seems a scale-similarity like assumption to evaluate the term (u')_bar. The u_bar filter and (u_bar)^ should be considered at level of the same filter width, from a numerical point of view. Even if it is stated that the "test filter" is at a width 2*Delta, the numerical procedure of averaging over adjacent cells would produce the same numerical filter width of the primary filter (which is implictly defined by the discretization).

The text stated that is a variation of the method, in the original Deardoff's procedure the k equation is solved.

Thank you, I didn't notice that there was written that is a variation. You are right also about the fact about the test filter. Then I cannot understand this choice. It is the square of the difference of two average. The one over 2*Delta is "affected by the filter with dimension Delta, so I cannot understand the sense of doing this.

[sbaffini]

Originally Posted by lucamirtanini

Thank you, I didn't notice that there was written that is a variation. You are right also about the fact about the test filter. Then I cannot understand this choice. It is the square of the difference of two average. The one over 2*Delta is "affected by the filter with dimension Delta, so I cannot understand the sense of doing this.

It is as simple as:

1) You need a SGS kinetic energy

2) You don't want to solve an equation for it

3) You compute the kinetic energy of the smallest resolved scales (i.e. between the test filter and the grid filter) and assume it is representative of the true SGS kinetic energy

It is used in the mixed scale model of Sagaut et al. and, indeed, based on the original idea of Cain and

J. Bardina, J.H. Ferziger, and W.C. Reynolds. Improved subgrid scale models for large eddy simulation. AIAA Paper, (80-1357), 1980

[FMDenaro]

Originally Posted by lucamirtanini

Thank you, I didn't notice that there was written that is a variation. You are right also about the fact about the test filter. Then I cannot understand this choice. It is the square of the difference of two average. The one over 2*Delta is "affected by the filter with dimension Delta, so I cannot understand the sense of doing this.

As addressed by Paolo, the approximation is in the evaluation of k from its definition instead that from the equation. Since u'=u-u_bar is unresolved, you can apply an explicit filter to the RHS to evaluate (u')filtered.

However, the numerical description of the filter provided in the page of FDS documentation can be largely debated, I don't agree with the method.