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POST User Guide
POST Version 9.6.1
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POST User Guide
POST Version 9.6.1
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Tasks related with post processing of data generated with ComputeStatistics.
Compute budget terms of the turbulent kinetic energy transport equation based on statistical moments. This means computing the trace of the terms calcStatisticsConvectionReynoldsStresses, calcStatisticsTurbulentDissipationRate,calcStatisticsTurbulentDissipationRateBasedOnBudget, calcStatisticsTurbulentProduction, calcStatisticsPressureStrain, calcStatisticsMassFlux, calcStatisticsMolecularDiffusion and calcStatisticsTurbulentDiffusion :
\[ \phi^{TKE} = \frac{1}{2} \left( \phi_{ii} \right) \]
Compute turbulent dissipation budget term of Reynolds stresses, which is defined as
\[ \epsilon_{ij} = \frac{1}{\overline{\rho}} \overline{ \sigma_{jk} \frac{\partial u_i^{\prime\prime}}{\partial x_k} + \sigma_{ik} \frac{\partial u_j^{\prime\prime}}{\partial x_k} } \]
Compute turbulent dissipation based on the imbalance of the favre-averaged Reynolds stress transport budget equation. This means subtracting the terms calcStatisticsTurbulentProduction, calcStatisticsPressureStrain, calcStatisticsMassFlux, calcStatisticsMolecularDiffusion and calcStatisticsTurbulentDiffusion from calcStatisticsConvectionReynoldsStresses :
\begin{eqnarray} \epsilon_{ij} &=& -\left(MC_{ij} - P_{ij} - \Pi_{ij} - M_{ij} - MD_{ij} - TD_{ij}\right) \\ &=& -\left( \frac{1}{\overline{\rho}} \frac{\partial \widetilde{u}_k \overline{\rho} \widetilde{u_i^{\prime\prime} u_j^{\prime\prime}}}{\partial x_k} - \left(- \left(\widetilde{u_i^{\prime\prime} u_k^{\prime\prime}} \frac{\partial \widetilde{u}_j}{\partial x_k} + \widetilde{u_j^{\prime\prime} u_k^{\prime\prime}} \frac{\partial \widetilde{u}_i}{\partial x_k} \right)\right) - \frac{1}{\overline{\rho}} \overline{ p^{\prime} \left( \frac{\partial u_i^{\prime\prime}}{\partial x_j} + \frac{\partial u_j^{\prime\prime}}{\partial x_i} \right)} -\frac{1}{\overline{\rho}} \left[ \overline{u_i^{\prime\prime}} \left( \frac{\partial \overline{\sigma_{jk}}}{\partial x_k} - \frac{\partial \overline{p}}{\partial x_j}\right) +\overline{u_j^{\prime\prime}} \left( \frac{\partial \overline{\sigma_{ik}}}{\partial x_k} - \frac{\partial \overline{p}}{\partial x_i}\right)\right] - \frac{1}{\overline{\rho}} \frac{\partial}{\partial x_k} \left( \overline{ \sigma_{jk}u_i^{\prime\prime} + \sigma_{ik}u_j^{\prime\prime} }\right) - \frac{1}{\overline{\rho}} \frac{\partial}{\partial x_k} \left( \overline{ \rho u_i^{\prime\prime} u_j^{\prime\prime} u_k^{\prime\prime}} - \overline{p^{\prime} u_i^{\prime\prime} \delta_{jk}} - \overline{p^{\prime} u_j^{\prime\prime} \delta_{ik}} \right) \right) \end{eqnarray}
Compute mass flux budget term of Reynolds stresses, which is defined as
\[ M_{ij} = \frac{1}{\overline{\rho}} \left[ \overline{u_i^{\prime\prime}} \left( \frac{\partial \overline{\sigma_{jk}}}{\partial x_k} - \frac{\partial \overline{p}}{\partial x_j}\right) +\overline{u_j^{\prime\prime}} \left( \frac{\partial \overline{\sigma_{ik}}}{\partial x_k} - \frac{\partial \overline{p}}{\partial x_i}\right)\right] \]
Compute mean convection budget term of Reynolds stresses, which is defined as
\[ MC_{ij} = \frac{1}{\overline{\rho}} \frac{\partial \widetilde{u}_k \overline{\rho} \widetilde{u_i^{\prime\prime} u_j^{\prime\prime}}}{\partial x_k} \]
Compute molecular diffusion budget term of Reynolds stresses, which is defined as
\[ MD_{ij} = \frac{1}{\overline{\rho}} \frac{\partial}{\partial x_k} \left( \overline{ \sigma_{jk}u_i^{\prime\prime} + \sigma_{ik}u_j^{\prime\prime} }\right) \]
Compute the Pope-Criterion [10] as an indicator of the required mesh resolution for LES.
\[ P = \frac{ k_{res} }{ k_{res} + k_{sgs} } \]
with [17] :
\[ k_{sgs} = \left( \frac{ \overline{\mu_t} }{ \widetilde{\rho} \Delta C_d } \right)^2 \]
| -cd | Value for model constant \(C_d\) (default 0.09). |
Compute pressure strain budget term of Reynolds stresses, which is defined as
\[ \Pi_{ij} = \frac{1}{\overline{\rho}} \overline{ p^{\prime} \left( \frac{\partial u_i^{\prime\prime}}{\partial x_j} + \frac{\partial u_j^{\prime\prime}}{\partial x_i} \right)} \]
Compute turbulent production budget term of Reynolds stresses, which is defined as
\[ P_{ij} = - \left(\widetilde{u_i^{\prime\prime} u_k^{\prime\prime}} \frac{\partial \widetilde{u}_j}{\partial x_k} + \widetilde{u_j^{\prime\prime} u_k^{\prime\prime}} \frac{\partial \widetilde{u}_i}{\partial x_k} \right) \]
Compute second moments of primitive variables:
| Name | Symbol |
|---|---|
| Reynolds stress tensor | \(\widetilde{u_i'' u_j''}\) |
| Density variance | \(\overline{\rho' \rho'}\) |
| Pressure variance | \(\overline{p' p'}\) |
Compute skewness
\[ \frac{\widetilde{u_i''^3}}{\widetilde{u_i''^2}^{\frac 3 2}} \]
and flatness
\[ \frac{\widetilde{u_i''^4}}{\widetilde{u_i''^2}^2} \]
Compute statistical moments from raw averages generated by ComputeStatistics with --averages. Tasks called are
Remove all raw averages generated by ComputeStatistics with --averages. This should be called after computeStatisticalValues to reduce the size of the output file.
Compute turbulent diffusion budget term of Reynolds stresses, which is defined as
\[ TD_{ij} = \frac{1}{\overline{\rho}} \frac{\partial}{\partial x_k} \left( \overline{ \rho u_i^{\prime\prime} u_j^{\prime\prime} u_k^{\prime\prime}} - \overline{p^{\prime} u_i^{\prime\prime} \delta_{jk}} - \overline{p^{\prime} u_j^{\prime\prime} \delta_{ik}} \right) \]
Compute Favre-averaged velocity vector
\[ \widetilde{u_i} \]
Compute Favre-averaged velocity gradient tensor
\[ \frac{\partial \widetilde{u}_i}{\partial x_j} \]
1.9.1