Statistical Uncertainty of DNS in Geometries without Homogeneous Directions
In this paper, we present uncertainties of statistical quantities of direct numerical simulations (DNS) with small numerical errors. The uncertainties are analysed for channel flow and a flow separation case in a confined backward facing step (BFS) geometry. The infinite channel flow case has two ho...
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MDPI AG
2021-02-01
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| author | Jure Oder Cédric Flageul Iztok Tiselj |
| author_facet | Jure Oder Cédric Flageul Iztok Tiselj |
| author_sort | Jure Oder |
| collection | DOAJ |
| description | In this paper, we present uncertainties of statistical quantities of direct numerical simulations (DNS) with small numerical errors. The uncertainties are analysed for channel flow and a flow separation case in a confined backward facing step (BFS) geometry. The infinite channel flow case has two homogeneous directions and this is usually exploited to speed-up the convergence of the results. As we show, such a procedure reduces statistical uncertainties of the results by up to an order of magnitude. This effect is strongest in the near wall regions. In the case of flow over a confined BFS, there are no such directions and thus very long integration times are required. The individual statistical quantities converge with the square root of time integration so, in order to improve the uncertainty by a factor of two, the simulation has to be prolonged by a factor of four. We provide an estimator that can be used to evaluate a priori the DNS relative statistical uncertainties from results obtained with a Reynolds Averaged Navier Stokes simulation. In the DNS, the estimator can be used to predict the averaging time and with it the simulation time required to achieve a certain relative statistical uncertainty of results. For accurate evaluation of averages and their uncertainties, it is not required to use every time step of the DNS. We observe that statistical uncertainty of the results is uninfluenced by reducing the number of samples to the point where the period between two consecutive samples measured in Courant–Friedrichss–Levy (CFL) condition units is below one. Nevertheless, crossing this limit, the estimates of uncertainties start to exhibit significant growth. |
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| language | English |
| last_indexed | 2024-03-09T05:47:23Z |
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| spelling | doaj.art-aa7ad0914c434bc1a75a2e0df639b5072023-12-03T12:19:55ZengMDPI AGApplied Sciences2076-34172021-02-01114139910.3390/app11041399Statistical Uncertainty of DNS in Geometries without Homogeneous DirectionsJure Oder0Cédric Flageul1Iztok Tiselj2Reactor Engineering Division, Jožef Stefan Institute, Jamova Cesta 39, SI-1000 Ljubljana, SloveniaCuriosity Group, Pprime Institute, Université de Poitiers, CNRS, ISAE-ENSMA-Téléport 2-Bd. Marie and Pierre Curie B.P. 30179, 86962 Futuroscope Chasseneuil CEDEX, FranceReactor Engineering Division, Jožef Stefan Institute, Jamova Cesta 39, SI-1000 Ljubljana, SloveniaIn this paper, we present uncertainties of statistical quantities of direct numerical simulations (DNS) with small numerical errors. The uncertainties are analysed for channel flow and a flow separation case in a confined backward facing step (BFS) geometry. The infinite channel flow case has two homogeneous directions and this is usually exploited to speed-up the convergence of the results. As we show, such a procedure reduces statistical uncertainties of the results by up to an order of magnitude. This effect is strongest in the near wall regions. In the case of flow over a confined BFS, there are no such directions and thus very long integration times are required. The individual statistical quantities converge with the square root of time integration so, in order to improve the uncertainty by a factor of two, the simulation has to be prolonged by a factor of four. We provide an estimator that can be used to evaluate a priori the DNS relative statistical uncertainties from results obtained with a Reynolds Averaged Navier Stokes simulation. In the DNS, the estimator can be used to predict the averaging time and with it the simulation time required to achieve a certain relative statistical uncertainty of results. For accurate evaluation of averages and their uncertainties, it is not required to use every time step of the DNS. We observe that statistical uncertainty of the results is uninfluenced by reducing the number of samples to the point where the period between two consecutive samples measured in Courant–Friedrichss–Levy (CFL) condition units is below one. Nevertheless, crossing this limit, the estimates of uncertainties start to exhibit significant growth.https://www.mdpi.com/2076-3417/11/4/1399turbulent flowDNSstatistical uncertaintypassive scalars |
| spellingShingle | Jure Oder Cédric Flageul Iztok Tiselj Statistical Uncertainty of DNS in Geometries without Homogeneous Directions Applied Sciences turbulent flow DNS statistical uncertainty passive scalars |
| title | Statistical Uncertainty of DNS in Geometries without Homogeneous Directions |
| title_full | Statistical Uncertainty of DNS in Geometries without Homogeneous Directions |
| title_fullStr | Statistical Uncertainty of DNS in Geometries without Homogeneous Directions |
| title_full_unstemmed | Statistical Uncertainty of DNS in Geometries without Homogeneous Directions |
| title_short | Statistical Uncertainty of DNS in Geometries without Homogeneous Directions |
| title_sort | statistical uncertainty of dns in geometries without homogeneous directions |
| topic | turbulent flow DNS statistical uncertainty passive scalars |
| url | https://www.mdpi.com/2076-3417/11/4/1399 |
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