1887
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Theoretically based optimal large-eddy simulation
Rent:
Rent this article for
USD
10.1063/1.3249754
/content/aip/journal/pof2/21/10/10.1063/1.3249754
http://aip.metastore.ingenta.com/content/aip/journal/pof2/21/10/10.1063/1.3249754

Figures

Image of FIG. 1.
FIG. 1.

Relative error in the quasinormal approximation to the nonzero elements of the fourth-order correlation , with separation in the direction. To obtain , the error in is normalized by . Due to isotropy 2 and 3 indices can be swapped with identical results.

Image of FIG. 2.
FIG. 2.

Generic stencil geometries for the stencil on a staggered grid, for use when estimating fluxes on the faces shown in gray. The stencil used here is obtained by adding a cell above and below the stencil shown on the left (in the direction).

Image of FIG. 3.
FIG. 3.

Relative error in estimating the dissipation from the longitudinal third-order structure function of a finite-volume filtered velocity field using Eq. (57). Filtered structure functions were computed by filtering the DNS at of Ref. 8. The filter was defined on a cubical finite-volume grid of the size noted, on a periodic domain of size . Each finite volume is of size , and is the offset between the volumes used to compute the structure function.

Image of FIG. 4.
FIG. 4.

Volumes (and their numbering) in a staggered grid stencil to estimate the flux through the surface between volumes −1 and 1. For the normal component flux , the volumes with solid outlines are on the -component mesh, and the dashed-outline volumes are not used. For the tangential-component flux , the solid volumes are on the -component mesh, and the dashed volumes are on the -component mesh. In Tables I, II, and V–VIII, the volumes are referred to by the numbers shown here, but no distinction is made between and because the values associated with these volumes are the same.

Image of FIG. 5.
FIG. 5.

The matrix norms and of the difference between the asymptotic kernels and the kernels at finite , as a function of .

Image of FIG. 6.
FIG. 6.

Three-dimensional energy spectra (a) and third-order structure functions (b) from OLES of isotropic turbulence at infinite Reynolds number using the finite- kernels, with resolutions ranging from to ( to , respectively). The solid lines in both plots are determined from the Kolmogorov theory. In (a), the two solid lines are a slope (shallow), and the result of filtering a spectrum. In (b) the straight line is , and the other solid line is the structure function of the filtered velocity determined from .

Image of FIG. 7.
FIG. 7.

Three-dimensional energy spectra (a) and third-order structure functions (b) from OLES of isotropic turbulence at infinite Reynolds number using both finite and asymptotic kernels (signified with “A”), with resolution and ( and , respectively). Solid lines in (a) and (b) are as in Fig. 6.

Image of FIG. 8.
FIG. 8.

Three-dimensional energy spectra (a) and third-order structure function (b) from LES of isotropic turbulence on a finite-volume grid at using the dynamic Smagorinsky model and finite- optimal models, with and stencils. Also shown is a filtered DNS. Numbers on the curve labels indicate the stencil size, 2 signifies the stencil, and 4 is the stencil.

Image of FIG. 9.
FIG. 9.

Spectra of the linear operators. Spectra have been scaled so that they are consistent approximations to the (negative) second derivative. Shown are the spectra for the asymptotic operators and those determined for a grid . and are the spectra for the and operators, respectively. Note that these operators are formulated to represent the flux in Eq. (2), which appear with a minus sign so a positive is dissipative.

Image of FIG. 10.
FIG. 10.

Bilinear spectra [(a)–(c)] and [(d)–(f)] . The spectra are for asymptotic optimal [(a) and (d)], optimal [(b) and (e)], and fourth-order operators [(c) and (f)]. Black contours are positive and gray are negative. The heavy contours indicate the zero level. Contour values are incremented by 0.3.

Image of FIG. 11.
FIG. 11.

The bilinear spectra for the normal quadratic operator along the diagonal . Shown are the spectra for the asymptotic operators , those determined for a grid , and those for a standard fourth-order operator. The vertical line at indicates the boundary between aliased (right) and unaliased (left) portions of the spectrum, and the dotted line is the spectrum of the exact Navier–Stokes operator.

Image of FIG. 12.
FIG. 12.

Three-dimensional energy spectra (a) and third-order structure functions (b) from OLES of isotropic turbulence at infinite Reynolds with resolution of . Compared are results using the finite kernels, asymptotic kernels (signified with A), and asymptotic kernels generated by neglecting the terms in Eqs. (63) and (67) (signified with “N”). Solid lines in (a) and (b) are as in Fig. 6.

Tables

Generic image for table
Table I.

Values of the elements of as determined for the stencil, with volume labels as defined in Fig. 4. The value of for volumes not listed here are determined from the symmetry .

Generic image for table
Table II.

Values of the elements of as determined for the stencil, with volume labels as defined in Fig. 4. The value of for volumes not listed here are determined from the symmetry .

Generic image for table
Table III.

Contributions to dissipation of the quadratic and linear portions of the asymptotic LES operators for flux of the normal momentum (normal) and tangential momentum (tangential). The sum signifies three times the normal contribution plus six times the tangential, which represents the contributions to the total dissipation of kinetic energy .

Generic image for table
Table IV.

Contributions to dissipation of the quadratic and linear portions of the asymptotic LES operators determined by neglecting the terms in Eqs. (63) and (67) for flux of the normal momentum (normal) and tangential momentum (tangential). The sum signifies three times the normal contribution plus six times the tangential, which represents the contributions to the total dissipation of kinetic energy .

Generic image for table
Table V.

Values of the elements of for a stencil, with volume labels as defined in Fig. 4. The values of for volumes not listed are determined from the symmetry .

Generic image for table
Table VI.

Values of the elements of and for a stencil. For and , volume label indicates a volume separated by volumes in the normal direction, with, for example, signifying and signifying the neighboring volume (in either direction). For , the volume labels are as defined in Fig. 4.

Generic image for table
Table VII.

Values of the elements of for a stencil, with volume labels as defined in Fig. 4. The value of for volumes not listed here are determined from the symmetry , the fact that is invariant with respect to permutation of the volume order, and that is invariant to a swap of and .

Generic image for table
Table VIII.

Values of the elements of , , and for a stencil, with volume labels as defined in Fig. 4. The value of for volumes not listed here is determined from the symmetry .

Loading

Article metrics loading...

/content/aip/journal/pof2/21/10/10.1063/1.3249754
2009-10-23
2014-04-16
Loading

Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Theoretically based optimal large-eddy simulation
http://aip.metastore.ingenta.com/content/aip/journal/pof2/21/10/10.1063/1.3249754
10.1063/1.3249754
SEARCH_EXPAND_ITEM