DNS 1-5 Quantification of Resolution

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Description

Computational Details

Quantification of Resolution

Statistical Data

Instantaneous Data

Storage Format

Quantification of 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 (${\Delta }$) with the characteristic lengths of the turbulence, i.e., the Taylor microscale (${\eta _{T}}$) and Kolmogorov length scale (${\eta _{K}}$). 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 $\left(V\right)$ and the number of DoFs $\left(N_{DoF}\right)$ within the mesh element per equation

$\Delta ={\sqrt[{3}]{\dfrac {V}{N_{DoF}}}}$

former relation is shown in Fig. 10 while the latter is reported in 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 ${\Delta /\eta _{K}\leq 5}$, as shown in Fig. 11.

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).

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).

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.

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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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