Bulletin of the American Physical Society
74th Annual Meeting of the APS Division of Fluid Dynamics
Volume 66, Number 17
Sunday–Tuesday, November 21–23, 2021; Phoenix Convention Center, Phoenix, Arizona
Session T02: Computational Fluid Dynamics: Uncertainty Quantification 
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Chair: Jeff Eldredge, UCLA Room: North 120 CD 
Tuesday, November 23, 2021 12:40PM  12:53PM 
T02.00001: A multifidelity approach to sensitivity estimation in large eddy simulation Walter AriasRamirez, Nikhil Oberoi, Johan Larsson An approach to compute approximate sensitivities in a large eddy simulation (LES) is proposed and assessed. The method is based on solving a linearized 
Tuesday, November 23, 2021 12:53PM  1:06PM 
T02.00002: Grid Tailored ReducedOrder Models for Steady Hypersonic Aerodynamics Patrick J Blonigan, David Ching, Marco Arienti, Francesco Rizzi, Jeffrey A Fike Highspeed aerospace engineering applications rely heavily on computational fluid dynamics (CFD) models for design and analysis due to the expense and difficulty of flight tests and experiments. This reliance on CFD necessitates performing accurate and reliable uncertainty quantification (UQ). However, CFD for hypersonic flows is very computationally expensive due to high grid resolution requirements. Additionally, UQ approaches are “manyquery” problems requiring many runs with a wide range of input parameters. 
Tuesday, November 23, 2021 1:06PM  1:19PM 
T02.00003: Uncertainty quantification and extreme event analysis for turbulent flows using energypreserving datadriven closure schemes AlexisTzianni Charalampopoulos, Themistoklis Sapsis We present a reducedorder modelling scheme for computing the statistics of incompressible turbulent flows. The scheme involves evolution equations for the mean and covariance of the system, in tandem with a neuralnetwork modelling of the higherorder closure terms. The closure terms are approximated using spatiotemporally nonlocal neuralnetworks with appropriate constraints enforced during training. These constraints allow the reducedorder model to adhere to the physical properties of the reference system. In more detail, energy preservation constraints ensure that the energy transfer between scales, as modelled by the nonlinear terms of the full system, are properly included in our model. The constraints are essential for our approximate model to reach the appropriate statistical equilibrium that corresponds to the full reference system. We showcase that our computationally tractable model is able to robustly approximate effectively complicated and expensive turbulent flows in the ocean and atmosphere. We test the method in its ability to approximate important statistics of these systems such as its mean and energy spectrum. We also approximate the probability density functions of quantities of interest, showing that the model can estimate the probability of intermittent extreme events occuring. Turbulent flows with Gaussian and strongly nonGaussian statistics are examined. 
Tuesday, November 23, 2021 1:19PM  1:32PM 
T02.00004: Simulating natural ventilation in buildings using CFD: Importance of thermal boundary conditions Lup Wai Chew, Chen Chen, Catherine Gorle For CFD simulations of natural ventilation in buildings, farfield thermal boundary conditions (BC) are often taken from nearby weather stations, while indoor surfaces are often assumed adiabatic. This study aims to quantify the errors that can be introduced by these assumptions. LES is used to simulate buoyancydriven ventilation in Stanford Y2E2 Building during a 3hour night flush with an initial indooroutdoor temperature difference of 4.0 K. Measured temperatures are used as BC and benchmark to quantify root mean square errors (RMSE) of LES results. The lowest RMSE of 0.36 K is achieved by prescribing the outdoor temperature measured on the building roof as the farfield temperature BC and prescribing the measured surface temperature as the thermal BC for the interior surfaces. Using the outdoor temperature from a weather station 1 km away as the farfield temperature BC increases the RMSE to 1.13 K. For the internal surfaces, the use of an adiabatic BC increases the RMSE to 1.73 K, showing that interior surfaces should not be assumed adiabatic. For prediction of natural ventilation using CFD, we suggest using outdoor temperature measured near a target building as the farfield thermal BC and measured or modeled surface temperatures as the thermal BC for internal surfaces. 
Tuesday, November 23, 2021 1:32PM  1:45PM 
T02.00005: Datadriven Eigenspace Perturbations for RANS Uncertainty Quantification Jan F Heyse, Nikita Kozak, Aashwin A Mishra, Gianluca Iaccarino Turbulence models are indispensable yet limited in their accuracy and therefore a significant source of modelform uncertainty in turbulent flow simulations. Datafree perturbations to the spectral decomposition of the Reynolds stress tensor can be used to obtain uncertainty envelopes for quantities of interest. Such datafree perturbations perturb at spatially uniform strength regardless of the expected local inaccuracy of the turbulence model. Since turbulence models work better in some situations than in others, this uniform approach tends to lead to an overestimation of the modelform uncertainty. 
Tuesday, November 23, 2021 1:45PM  1:58PM 
T02.00006: Turbulence Model Form Errors in a Statistically Stationary Separation Bubble Kerry S Klemmer, Wen Wu, Michael E Mueller Model form error arises from physical assumptions made in constructing models either to reduce the physical complexity or to model physical processes that are not well understood. In turbulence modeling, specifically Reynolds stress modeling, model form errors result from the Boussinesq hypothesis and other modeling choices, such as the specific form of the eddy viscosity. These linear eddy viscosity models have known points of failure in flows that introduce complex strain, such as separated flows. In this work, an "implied models" approach is used to better understand the sources and dynamics of model form error in separated flows. In the "implied models" approach, a transport equation is derived for the model error through the transport equation implied by the model for the quantity of interest. A boundary layer over a flat plate with a statistically stationary separation bubble is analyzed and shown to have two error modes corresponding to the qualitative behavior of turbulent wallbounded and turbulent freeshear model form errors, which have previously been analyzed. These results indicate a complex picture of model error that changes through the flow but also that calibration of turbulence models against simpler canonical flows may capture the main modes of model failure. 
Tuesday, November 23, 2021 1:58PM  2:11PM 
T02.00007: Exploring Machine Learning Strategies for RANS Uncertainty Quantification Nikita Kozak, Jan F Heyse, Aaswhin Ananda Mishra, Gianluca Iaccarino This work builds the understanding of the critical machine learning considerations when predicting the uncertainty bounds for a Reynolds Averaged NaiverStokes (RANS) model. These bounds are created with eigenvalue perturbations to the Reynolds stress anisotropy tensor, predicted by a random forest trained on highfidelity data that exhibits similar flow characteristics to those being studied with the lowfidelity approach. The first part of this work explores the hyperparameters of the random forest, the utilization of weak learners, and the optimal strategy for training applied to an asymmetric diffuser. This exploration provided insight into the random forests' sensitivity to different variables and dataset divisions, and the overall accuracy of eigenvalue perturbations. These insights led to restructuring the machine learning approach to two separate objectives summarized as a classification and regression problem. We seek to classify different areas of the flow field into universal regimes and then determine how much to perturb the corresponding fields from the classified insights and other flow characteristics. The second part of this work introduces the classification aspect with primary results applied to an asymmetric diffuser, jetdata, and other compressible flows. 
Tuesday, November 23, 2021 2:11PM  2:24PM 
T02.00008: Potential flows: a playground for nonlocal and nonlinear inference problems Mathieu Le Provost, Ricardo Baptista, Youssef Marzouk, Jeff D Eldredge An accurate estimation of the flow field from limited and noisy observations is crucial in many fields of engineering. To tackle these inverse problems, classical localization schemes suppress correlations at long distances. However, these techniques are not well suited for incompressible fluid problems, in which the observations are typically obtained by nonlocal and nonlinear mappings of the state, e.g. the pressure Poisson equation. Instead these inference problems have lowrank structure in the sense that lowdimensional projections of the observations are most informative of a lowdimensional subspace of the state space. Thus, interactions between state and observation variables are best described as clusters of variables, reminiscent of the fast multipole method (FMM). To drive further research in this area, we show that potential flow problems constitute a nice playground to experiment with nonlocal and nonlinear inference problems, while allievating the highdimensionality of a standard incompressible fluid problem. Indeed, estimating the position and strength of a handful of singularities (e.g. vortices, sources) from pressure observations distills the main features of a realistic inverse problem. To exploit the lowrank structure, we present a systematic procedure to identify these clusters of variables from the sensitivity analysis of the observation operator. We also explore connections between the proposed sensitivity analysis and the FMM. Finally, we present recent advances in nonlinear priortoposterior transformations to perform consistent inference with nonlinear statespace models. 
Tuesday, November 23, 2021 2:24PM  2:37PM 
T02.00009: A computationally affordable multifidelity approach to parametric studies Nikhil Oberoi, Walter AriasRamirez, Johan Larsson

Tuesday, November 23, 2021 2:37PM  2:50PM 
T02.00010: Multiphase flow applications of nonintrusive reducedorder models with Gaussian process emulation Themistoklis Botsas, Lachlan Mason, Indranil Pan, Omar K Matar Reducedorder models are computationally inexpensive simplifications of highfidelity complex models. Such models can be found in computational fluid dynamics, e.g. in multiphase flow applications. We present a reducedorder model analysis framework where we couple compression techniques such as autoencoders with Gaussian process regression, and its natural extension: the Deep Gaussian Process (DGP) in the latent space. The mixture has some significant advantages as opposed to the standard encodingdecoding routine, primarily, the ability to interpolate or extrapolate in the initial conditions, which can offer results even when simulations are unavailable. We compare the methodology with alternative interpolation algorithms (long shortterm memories) using exemplars from multiphase flow applications, and we examine how each variation affects our analysis. 
Tuesday, November 23, 2021 2:50PM  3:03PM 
T02.00011: Hierarchical multifidelity models for the simulation of turbulent flows Saleh Rezaeiravesh, Timofey Mukha, Ricardo Vinuesa, Philipp Schlatter Numerical simulations of turbulent flows are of utmost importance in physics and engineering. In practice, for a given computational budget an efficient strategy is required to address the socalled "outerloop problem", such as flow prediction, uncertainty quantification and optimization, which typically demand multiple simulations. The present study reports our recent progress on further development and implementation of a class of hierarchical multifidelity models (MFMs) which allow for simultaneous calibration of uncertain parameters. In a Bayesian framework, at each fidelity level both model inadequacy and aleatoric uncertainties are considered. The developed MFM is applied to different flow problems as examples: i) prediction of wing polars for a standard airfoil where the angle of attack is the design parameter, and, ii) propagation of geometrical uncertainties into the quantities of interest of the turbulent flow over a periodic hill. In all problems, the predictions by the MFM are validated and the associated uncertainty is determined. The hierarchical MFM is shown to be compatible with the hierarchy of the turbulence modeling approaches and also capable of accurately handling the outerloop problems with minimal computational cost. 
Tuesday, November 23, 2021 3:03PM  3:16PM 
T02.00012: Reliable quantification of uncertainty in time averages of turbulence simulations Donnatella G Xavier, Saleh Rezaeiravesh, Ricardo Vinuesa, Philipp Schlatter Estimation of uncertainties in timeaveraged quantities of turbulence simulations requires statistical tools that take into account the temporal correlation within the data. This is the key result in our validation of the commonly used uncertainty estimators for turbulence time averages i.e., batchmeans methods and autoregressive model (ARM) based estimators. The validation enabled us to derive novel guidelines for the choice of the hyperparameters intrinsic to these methods, such as the batch size in the batchmeans methods and the order of the ARM model, in terms of turbulence timescales. Our study also revealed that the ARM estimator could be made to retain information through the autocorrelation exactly up to a given point in time by the combination of the model order and covered time lag. This property preserved the accuracy of the estimator even upon downsampling or batching the time series, thereby allowing computationally efficient implementations. We also address the need for including expected values of nonlinear components in the uncertainty quantification (UQ) of higherorder statistics, an aspect often neglected in the UQ/turbulence literature. The UQ analyses are performed using the time series of turbulent channel and periodic hill flow. 
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