DNS 1-5 Quantification of Resolution: Difference between revisions

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= Quantification of resolution =
= Quantification of resolution =
==Mesh resolution==
==Mesh resolution==
Provide wall resolution in wall coordinates, both normally ("y+") and tangentially ("x+", "z+").
Evaluate typical turbulence length scales (Taylor microscale, Kolmogorov) and compare to local
resolution. In case the case presents homogeneous directions, one could also provide spatial
correlations between the velocity components. If possible provide computed temporal spectra at
selected locations and relate to spatial resolution e.g. by using Taylor's hypothesis.
The mesh resolution is quantified by comparing the mesh characteristic length (<math>{\Delta}</math>) with the characteristic lengths of the turbulence, i.e., the Taylor microscale (<math>{\eta_T}</math>) and Kolmogorov length scale (<math>{\eta_K}</math>).
The mesh resolution is quantified by comparing the mesh characteristic length (<math>{\Delta}</math>) with the characteristic lengths of the turbulence, i.e., the Taylor microscale (<math>{\eta_T}</math>) and Kolmogorov length scale (<math>{\eta_K}</math>).
Here, the mesh characteristic length takes into account of the degree of the DG polynomial approximation. In particular, it is defined as the cubic root of the ratio between the mesh element volume <math>\left(V\right)</math> and the number of DoFs <math>\left(N_{DoF}\right)</math> within the mesh element per equation
Here, the mesh characteristic length takes into account of the degree of the DG polynomial approximation. In particular, it is defined as the cubic root of the ratio between the mesh element volume <math>\left(V\right)</math> and the number of DoFs <math>\left(N_{DoF}\right)</math> within the mesh element per equation
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<math>\Delta=\sqrt[3]{\dfrac{V}{N_{DoF}}}</math>
<math>\Delta=\sqrt[3]{\dfrac{V}{N_{DoF}}}</math>


former relation is shown in [[lib:DNS_1-3_quantification_#figure10|Fig. 10]] while the latter is reported in [[lib:DNS_1-3_quantification_#figure11|Fig. 11]]. As it can be seen, both relations indicate that the resolution achieved by the present grid is at DNS level. In particular, it is commonly accepted that DNS is achieved when <math>{\Delta/\eta_K \leq 5}</math>, as shown in [[lib:DNS_1-3_quantification_#figure11|Fig. 11]].
The comparison with respect to the Taylor microscale is shown in [[lib:DNS1-5_quantification_Taylor_#figure3|Fig. 3]]. The maximum ratio <math>{\Delta}/{\eta_{T}}</math> within the outer layer of the boundary layer is approximately 0.4.
 
In [[lib:DNS1-5_quantification_Kolmogorov_#figure4|Fig. 4]] is reported the comparison with respect to the Kolmogorov length scale. Above the flat plate upstream the rounded step the ratio <math>{\Delta}/{\eta_{K}}</math> is below 5.5, while above the rounded step is lower than 7.5.


<div id="figure3"></div>
<div id="figure3"></div>
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|align="center"|'''Figure 3:''' Rounded step case, Re=78490. Relation between the mesh size and the Taylor microscale at midspan using MIGALE with DG P3 (~300 million DoF/eqn).
|align="center"|'''Figure 3:''' Rounded step case, Re=78490. Relation between the mesh size and the Taylor microscale at midspan using MIGALE with DG P3 (~300 million DoF/eqn).
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<div id="figure4"></div>
<div id="figure4"></div>
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|align="center"|'''Figure 4:''' Rounded step case, Re=78490. Relation between the mesh size and the Kolmogorov length scale at midspan using MIGALE with DG P3 (~300 million DoF/eqn).
|align="center"|'''Figure 4:''' Rounded step case, Re=78490. Relation between the mesh size and the Kolmogorov length scale at midspan using MIGALE with DG P3 (~300 million DoF/eqn).
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The average wall resolution at the checkpoint location <math>\left(x_{ref}/H=-3.5\right)</math> is <math>x^{+}=18</math> in stream direction, <math>y_{1}^{+}=1</math> in normal direction, and <math>z^{+}=19.5</math> in span direction.


==Solution verification==
==Solution verification==

Revision as of 14:56, 22 November 2022


Front Page

Description

Computational Details

Quantification of Resolution

Statistical Data

Instantaneous Data

Storage Format

Quantification of resolution

Mesh resolution

The mesh resolution is quantified by comparing the mesh characteristic length () with the characteristic lengths of the turbulence, i.e., the Taylor microscale () and Kolmogorov length scale (). Here, the mesh characteristic length takes into account of the degree of the DG polynomial approximation. In particular, it is defined as the cubic root of the ratio between the mesh element volume and the number of DoFs within the mesh element per equation

The comparison with respect to the Taylor microscale is shown in Fig. 3. The maximum ratio within the outer layer of the boundary layer is approximately 0.4. In Fig. 4 is reported the comparison with respect to the Kolmogorov length scale. Above the flat plate upstream the rounded step the ratio is below 5.5, while above the rounded step is lower than 7.5.

DNS1-5 rounded step Taylor scale.png
Figure 3: Rounded step case, Re=78490. Relation between the mesh size and the Taylor microscale at midspan using MIGALE with DG P3 (~300 million DoF/eqn).
DNS1-5 rounded step Kolmogorov scale.png
Figure 4: Rounded step case, Re=78490. Relation between the mesh size and the Kolmogorov length scale at midspan using MIGALE with DG P3 (~300 million DoF/eqn).

The average wall resolution at the checkpoint location is in stream direction, in normal direction, and in span direction.

Solution verification

One way to verify that the DNS are properly resolved is to examine the residuals of the Reynolds- stress budget equations. These residuals are among the statistical volume data to be provided as described in Statistical Data section.


Contributed by: Francesco Bassi, Alessandro Colombo, Francesco Carlo Massa — Università degli studi di Bergamo (UniBG)

Front Page

Description

Computational Details

Quantification of Resolution

Statistical Data

Instantaneous Data

Storage Format


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