https://sam.ensam.eu:443 The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material. Sat, 14 Mar 2026 22:34:02 GMT 2026-03-14T22:34:02Z 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 GMT http://hdl.handle.net/10985/15497 2018-01-01T00:00:00Z 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. http://hdl.handle.net/10985/15556 Data-Driven Deterministic Symbolic Regression of Nonlinear Stress-Strain Relation for RANS Turbulence Modelling SCHMELZER, Martin; DWIGHT, Richard P.; CINNELLA, Paola This work presents developments towards a deterministic symbolic regression method to derive algebraic Reynolds-stress models for the Reynolds-Averaged Navier-Stokes (RANS) equations. The models are written as tensor polynomials, for which optimal coe cients are found using Bayesian inversion. These coe cient fields are the targets for the symbolic regression. A method is presented based on a regularisation strategy in order to promote sparsity of the inferred models and is applied to high-fidelity data. By being data-driven the method reduces the assumptions commonly made in the process of model development in order to increase the predictive fidelity of algebraic models. Mon, 01 Jan 2018 00:00:00 GMT http://hdl.handle.net/10985/15556 2018-01-01T00:00:00Z SCHMELZER, Martin DWIGHT, Richard P. CINNELLA, Paola This work presents developments towards a deterministic symbolic regression method to derive algebraic Reynolds-stress models for the Reynolds-Averaged Navier-Stokes (RANS) equations. The models are written as tensor polynomials, for which optimal coe cients are found using Bayesian inversion. These coe cient fields are the targets for the symbolic regression. A method is presented based on a regularisation strategy in order to promote sparsity of the inferred models and is applied to high-fidelity data. By being data-driven the method reduces the assumptions commonly made in the process of model development in order to increase the predictive fidelity of algebraic models. http://hdl.handle.net/10985/23745 CFD-driven symbolic identification of algebraic Reynolds-stress models BEN HASSAN SAIDI, Ismaïl; SCHMELZER, Martin; CINNELLA, Paola; GRASSO, Francesco Reynolds-stress models (EARSM) from high-fidelity data is developed building on the frozen-training SpaRTA algorithm of [1]. Corrections for the Reynolds stress tensor and the production of transported turbulent quantities of a baseline linear eddy viscosity model (LEVM) are expressed as functions of tensor polynomials selected from a library of candidate functions. The CFD-driven training consists in solving a blackbox optimization problem in which the fitness of candidate EARSM models is evaluated by running RANS simulations. The procedure enables training models against any target quantity of interest, computable as an output of the CFD model. Unlike the frozen-training approach, the proposed methodology is not restricted to data sets for which full fields of high-fidelity data, including second flow order statistics, are available. However, the solution of a high-dimensional expensive blackbox function optimization problem is required. Several steps are then undertaken to reduce the associated computational burden. First, a sensitivity analysis is used to identify the most influential terms and to reduce the dimensionality of the search space. Afterwards, the Constrained Optimization using Response Surface (CORS) algorithm, which approximates the black-box cost function using a response surface constructed from a limited number of CFD solves, is used to find the optimal model parameters. Model discovery and cross-validation is performed for three configurations of 2D turbulent separated flows in channels of variable section using different sets of training data to show the flexibility of the method. The discovered models are then applied to the prediction of an unseen 2D separated flow with higher Reynolds number and different geometry. The predictions of the discovered models for the new case are shown to be not only more accurate than the baseline LEVM, but also of a multi-purpose EARSM model derived from purely physical arguments. The proposed deterministic symbolic identification approach constitutes a promising candidate for building accurate and robust RANS models customized for a given class of flows at moderate computational cost. ©2022 Elsevier Inc. All rights reserved. Tue, 01 Feb 2022 00:00:00 GMT http://hdl.handle.net/10985/23745 2022-02-01T00:00:00Z BEN HASSAN SAIDI, Ismaïl SCHMELZER, Martin CINNELLA, Paola GRASSO, Francesco Reynolds-stress models (EARSM) from high-fidelity data is developed building on the frozen-training SpaRTA algorithm of [1]. Corrections for the Reynolds stress tensor and the production of transported turbulent quantities of a baseline linear eddy viscosity model (LEVM) are expressed as functions of tensor polynomials selected from a library of candidate functions. The CFD-driven training consists in solving a blackbox optimization problem in which the fitness of candidate EARSM models is evaluated by running RANS simulations. The procedure enables training models against any target quantity of interest, computable as an output of the CFD model. Unlike the frozen-training approach, the proposed methodology is not restricted to data sets for which full fields of high-fidelity data, including second flow order statistics, are available. However, the solution of a high-dimensional expensive blackbox function optimization problem is required. Several steps are then undertaken to reduce the associated computational burden. First, a sensitivity analysis is used to identify the most influential terms and to reduce the dimensionality of the search space. Afterwards, the Constrained Optimization using Response Surface (CORS) algorithm, which approximates the black-box cost function using a response surface constructed from a limited number of CFD solves, is used to find the optimal model parameters. Model discovery and cross-validation is performed for three configurations of 2D turbulent separated flows in channels of variable section using different sets of training data to show the flexibility of the method. The discovered models are then applied to the prediction of an unseen 2D separated flow with higher Reynolds number and different geometry. The predictions of the discovered models for the new case are shown to be not only more accurate than the baseline LEVM, but also of a multi-purpose EARSM model derived from purely physical arguments. The proposed deterministic symbolic identification approach constitutes a promising candidate for building accurate and robust RANS models customized for a given class of flows at moderate computational cost. ©2022 Elsevier Inc. All rights reserved. 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 GMT http://hdl.handle.net/10985/15499 2019-07-01T00:00:00Z SCHMELZER, Martin DWIGHT, Richard P. EDELING, Wouter Nico CINNELLA, Paola