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http://hdl.handle.net/10985/10077
Bayesian estimates of parameter variability in the k − ε turbulence model
EDELING, Wouter Nico; CINNELLA, Paola; DWIGHT, Richard P.; BIJL, H.
In this paper we are concerned with obtaining estimates for the error in Reynolds-Averaged Navier-Stokes (RANS) simulations based on the Launder-Sharma k−ε turbulence closure model, for a limited class of flows. In particular we search for estimates grounded in uncertainties in the space of model closure coeffi-cients, for wall-bounded flows at a variety of favourable and adverse pressure gradients. In order to estimate the spread of closure coefficients which repro-duces these flows accurately, we perform 13 separate Bayesian calibrations – each at a different pressure gradient – using measured boundary-layer velocity profiles, and a statistical model containing a multiplicative model inadequacy term in the solution space. The results are 13 joint posterior distributions over coefficients and hyper-parameters. To summarize this information we compute Highest Posterior-Density (HPD) intervals, and subsequently represent the to-tal solution uncertainty with a probability-box (p-box). This p-box represents both parameter variability across flows, and epistemic uncertainty within each calibration. A prediction of a new boundary-layer flow is made with uncer-tainty bars generated from this uncertainty information, and the resulting error estimate is shown to be consistent with measurement data.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10985/100772014-01-01T00:00:00ZEDELING, Wouter NicoCINNELLA, PaolaDWIGHT, Richard P.BIJL, H.In this paper we are concerned with obtaining estimates for the error in Reynolds-Averaged Navier-Stokes (RANS) simulations based on the Launder-Sharma k−ε turbulence closure model, for a limited class of flows. In particular we search for estimates grounded in uncertainties in the space of model closure coeffi-cients, for wall-bounded flows at a variety of favourable and adverse pressure gradients. In order to estimate the spread of closure coefficients which repro-duces these flows accurately, we perform 13 separate Bayesian calibrations – each at a different pressure gradient – using measured boundary-layer velocity profiles, and a statistical model containing a multiplicative model inadequacy term in the solution space. The results are 13 joint posterior distributions over coefficients and hyper-parameters. To summarize this information we compute Highest Posterior-Density (HPD) intervals, and subsequently represent the to-tal solution uncertainty with a probability-box (p-box). This p-box represents both parameter variability across flows, and epistemic uncertainty within each calibration. A prediction of a new boundary-layer flow is made with uncer-tainty bars generated from this uncertainty information, and the resulting error estimate is shown to be consistent with measurement data.Simplex-stochastic collocation method with improved scalability
http://hdl.handle.net/10985/15517
Simplex-stochastic collocation method with improved scalability
EDELING, Wouter Nico; DWIGHT, Richard P.; CINNELLA, Paola
The Simplex-Stochastic Collocation (SSC) method is a robust tool used to propagate uncertain input distributions through a computer code. However, it becomes prohibitively expensive for problems with dimensions higher than 5. The main purpose of this paper is to identify bottlenecks, and to improve upon this bad scalability. In order to do so, we propose an alternative interpolation stencil technique based upon the Set-Covering problem, and we integrate the SSC method in the High-Dimensional Model-Reduction framework. In addition, we address the issue of ill-conditioned sample matrices, and we present an analytical map to facilitate uniformly-distributed simplex sampling.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10985/155172016-01-01T00:00:00ZEDELING, Wouter NicoDWIGHT, Richard P.CINNELLA, PaolaThe Simplex-Stochastic Collocation (SSC) method is a robust tool used to propagate uncertain input distributions through a computer code. However, it becomes prohibitively expensive for problems with dimensions higher than 5. The main purpose of this paper is to identify bottlenecks, and to improve upon this bad scalability. In order to do so, we propose an alternative interpolation stencil technique based upon the Set-Covering problem, and we integrate the SSC method in the High-Dimensional Model-Reduction framework. In addition, we address the issue of ill-conditioned sample matrices, and we present an analytical map to facilitate uniformly-distributed simplex sampling.Bayesian Predictions of Reynolds-Averaged Navier–Stokes Uncertainties Using Maximum a Posteriori Estimates
http://hdl.handle.net/10985/15497
Bayesian Predictions of Reynolds-Averaged Navier–Stokes Uncertainties Using Maximum a Posteriori Estimates
CINNELLA, Paola; SCHMELZER, Martin; EDELING, Wouter Nico
Computational fluid dynamics analyses of high-Reynolds-number flows mostly rely on the Reynolds-averaged Navier–Stokes equations. The associated closure models are based on multiple simplifying assumptions and involve numerous empirical closure coefficients, which are calibrated on a set of simple reference flows. Predicting new flows using a single closure model with nominal values for the closure coefficients may lead to biased predictions. Bayesian model-scenario averaging is a statistical technique providing an optimal way to combine the predictions of several competing models calibrated on various sets of data (scenarios). The method allows a stochastic estimate of a quantity of interest in an unmeasured prediction scenario to be obtain by 1) propagating posterior probability distributions of the parameters obtained for multiple calibration scenarios, and 2) computing a weighted posterior predictive distribution. Although step 2 has a negligible computational cost, step 1 requires a large number of samples of the solver. To enable the application of the proposed approach to computationally expensive flow configurations, a modified formulation is used where a maximum posterior probability approximation is used to drastically reduce the computational burden. The predictive capability of the proposed simplified approach is assessed for two-dimensional separated and three-dimensional compressible flows.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/154972018-01-01T00:00:00ZCINNELLA, PaolaSCHMELZER, MartinEDELING, Wouter NicoComputational fluid dynamics analyses of high-Reynolds-number flows mostly rely on the Reynolds-averaged Navier–Stokes equations. The associated closure models are based on multiple simplifying assumptions and involve numerous empirical closure coefficients, which are calibrated on a set of simple reference flows. Predicting new flows using a single closure model with nominal values for the closure coefficients may lead to biased predictions. Bayesian model-scenario averaging is a statistical technique providing an optimal way to combine the predictions of several competing models calibrated on various sets of data (scenarios). The method allows a stochastic estimate of a quantity of interest in an unmeasured prediction scenario to be obtain by 1) propagating posterior probability distributions of the parameters obtained for multiple calibration scenarios, and 2) computing a weighted posterior predictive distribution. Although step 2 has a negligible computational cost, step 1 requires a large number of samples of the solver. To enable the application of the proposed approach to computationally expensive flow configurations, a modified formulation is used where a maximum posterior probability approximation is used to drastically reduce the computational burden. The predictive capability of the proposed simplified approach is assessed for two-dimensional separated and three-dimensional compressible flows.Data-Free and Data-Driven RANS Predictions with Quantified Uncertainty
http://hdl.handle.net/10985/15564
Data-Free and Data-Driven RANS Predictions with Quantified Uncertainty
EDELING, Wouter Nico; IACCARINO, Gianluca; CINNELLA, Paola
For the purpose of estimating the epistemic model-form uncertainty in Reynolds-Averaged Navier-Stokes closures, we propose two transport equations to locally perturb the Reynolds stress tensor of a given baseline eddy-viscosity model. The spatial structure of the perturbations is determined by the proposed transport equations, and thus does not have to be inferred from full-field reference data. Depending on a small number of model parameters and the local flow conditions, a ’return to eddy viscosity’ is described, and the underlying baseline state can be recovered. In order to make predictions with quantified uncertainty, we identify two separate methods, i.e. a data-free and data-driven approach. In the former no reference data is required and computationally inexpensive intervals are computed. When reference data is available, Bayesian inference can be applied to obtained informed distributions of the model parameters and simulation output.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/155642017-01-01T00:00:00ZEDELING, Wouter NicoIACCARINO, GianlucaCINNELLA, PaolaFor the purpose of estimating the epistemic model-form uncertainty in Reynolds-Averaged Navier-Stokes closures, we propose two transport equations to locally perturb the Reynolds stress tensor of a given baseline eddy-viscosity model. The spatial structure of the perturbations is determined by the proposed transport equations, and thus does not have to be inferred from full-field reference data. Depending on a small number of model parameters and the local flow conditions, a ’return to eddy viscosity’ is described, and the underlying baseline state can be recovered. In order to make predictions with quantified uncertainty, we identify two separate methods, i.e. a data-free and data-driven approach. In the former no reference data is required and computationally inexpensive intervals are computed. When reference data is available, Bayesian inference can be applied to obtained informed distributions of the model parameters and simulation output.Estimation of Model Error Using Bayesian Model-Scenario Averaging with Maximum a Posterori-Estimates
http://hdl.handle.net/10985/15499
Estimation of Model Error Using Bayesian Model-Scenario Averaging with Maximum a Posterori-Estimates
SCHMELZER, Martin; DWIGHT, Richard P.; EDELING, Wouter Nico; CINNELLA, Paola
Mon, 01 Jul 2019 00:00:00 GMThttp://hdl.handle.net/10985/154992019-07-01T00:00:00ZSCHMELZER, MartinDWIGHT, Richard P.EDELING, Wouter NicoCINNELLA, Paola