Quantification of resolution

Mesh resolution

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

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

The comparison with respect to the Taylor microscale is shown in Fig. 3. The maximum ratio ${\Delta }/{\eta _{T}}$ 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 ${\Delta }/{\eta _{K}}$ is below 5.5, while above the rounded step is lower than 7.5.

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).

The average wall resolution at the checkpoint location $\left(x_{ref}/H=-3.5\right)$ is $x^{+}=18$ in stream direction, $y_{1}^{+}=1$ in normal direction, and $z^{+}=19.5$ 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)

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Description

Computational Details

Quantification of Resolution

Statistical Data

Instantaneous Data

Storage Format