Bulletin of the American Physical Society
71st Annual Meeting of the APS Division of Fluid Dynamics
Volume 63, Number 13
Sunday–Tuesday, November 18–20, 2018; Atlanta, Georgia
Session Q32: Uncertainty Quantification 
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Chair: Gianluca Iaccarino, Stanford University Room: Georgia World Congress Center B404 
Tuesday, November 20, 2018 12:50PM  1:03PM 
Q32.00001: Bayesian optimization of RANS simulation with Ensemble based Variational method in convergentdivergent channel Xinlei Zhang, Olivier CoutierDelgosha, Thomas Gomez, Heng Xiao This work investigates the applicability of hybrid data assimilation approach to optimize RANS simulation in convergentdivergent channel from perspective of quantifying and reducing the uncertainty of inlet velocity and turbulence model. Specifically, the ensemble based variational method is applied to infer the inlet velocity and turbulent model corrections by assimilating DNS resolutions or limited experimental data. The approach is firstly adopted to infer the inlet velocity profile for the bump and Venturi geometry. The improvement can be achieved at the inlet region for the bump, but for Venturi in light of the limited measurements in APG region, the perturbation of inlet velocity is not sensitive to the observation space. Further the model corrections in kw SST model are investigated by assimilating the limited sparse experimental data. The improvements can be achieved for both velocity and turbulent kinetic energy(TKE). The results indicate that ensemble based variational method is capable of inferring unknown quantities of both low dimension (D=20) and high dimension (D=2400) with small ensemble size robustly and nonintrusively. This approach can be a good unity for the Bayesian inference or optimization in CFD problems. 
Tuesday, November 20, 2018 1:03PM  1:16PM 
Q32.00002: Intrusive uncertainty quantification of relevant multiphase flows: assessment of the multiUQ framework Brian Turnquist, Mark F Owkes Current direct numerical simulations of the NavierStokes equations for multiphase flow assume known initial and boundary conditions. However, due to potential variability in boundary conditions and measurement error in fluid characteristics, this assumption results in a simplification of the problem. Uncertainty quantification (UQ) is a tool that measures how input uncertainty propagates through a system and manifests in output. Extracting statistical information from a UQ solver offers greater understanding of how variables interact in a nonlinear fluid system, potentially improving engineering designs. MonteCarlo sampling is a common form of nonintrusive UQ, which is straightforward to implement. Intrusive UQ methods exist, including those used in the multiUQ framework, which are more computationally efficient. In this work, details of an intrusive multiphase UQ method are provided which require including uncertain variables in the governing equations and rewriting numerical methods. Computational cost of the method is compared to MonteCarlo. The method is applied to an oscillating droplet, falling water droplet, and an atomizing jet to demonstrate the usefulness of the technique and assess the sensitivity of outputs to multiple input uncertainties using Sobol indices. 
Tuesday, November 20, 2018 1:16PM  1:29PM 
Q32.00003: Quantification of uncertainty due to spectral parameterization of topography in deepocean lee waves Peiyun Zhu, Frederick Mayer, Oliver B Fringer, Catherine Gorle Stratified, steady geostrophic flow impinging on bottom topography generates oceanic lee waves. Their generation causes drag on the current, which is often parameterized in global circulation models with use of the topographic spectrum. Because a significant portion of the ocean floor is unmapped at resolutions sufficient to generate lee waves, a spectral model of the dominant bathymetric feature, the abyssal hills, is used. This study aims to quantify the uncertainty of lee wave drag prediction associated with the spectral model, which involves five uncertain physical parameters. We use three models along with the spectral model to compute wave drag: Linear theory, inviscid nonlinear theory (Long’s model) and CFD (using the SUNTANS ocean model). For each of the three models, we test the sensitivity of the five parameters in the spectral model. In SUNTANS simulations, we apply the spectral model by inverting a regional multibeam bathymetric dataset. Comparing uncertainties in wave drag of the three simulation sets will shed light on how uncertainty propagates from the topographic spectrum to the lee wave flow field, and thus guide the parameterization of lee waves in global circulation models. 
Tuesday, November 20, 2018 1:29PM  1:42PM 
Q32.00004: Stochastic Approaches to Quantify Solution Sensitivity to the Grid Timothy P Gallagher Quantifying grid convergence is an essential component of predictive and reliable computational simulation. For many problems of practical interest involving tens of millions to hundreds of millions of degrees of freedom, this process is often impractical. Furthermore, techniques like implicitlyfiltered Large Eddy Simulation lack a clear definition of grid convergence and only reach grid independence in a limit that is impossible to reach for relevant Reynolds numbers. In this work, an alternative process to assess the sensitivity of the solution to the grid is developed by treating the grid as a stochastic mesh. Rules based on allowable metrics, such as maximum stretching ratios, maximum skewness, etc., create correlations between the grid points, creating a system of dependent random variables. Novel nonintrusive, intrusive, and hybrid techniques to solve for the solution statistics using a stochastic mesh will be evaluated on representative problems. The result is a technique that can be used to guide improvements to the grid or that can serve as an alternative to quantifying grid convergence. 
Tuesday, November 20, 2018 1:42PM  1:55PM 
Q32.00005: Analysis of uncertainty of a heated pool via reduced order modelling Andreas G Class, Jorge Yanez In this article the uncertainty on the calculation of three dimensional spatiotemporal evolution of RaileighBènard convection is analyzed. This assessment is carried out through the creation of a surrogate fast model for the thermal natural convection of pools. The assessment of the inaccuracy and sensitivity of simulations of natural convection in pools is of the highest importance for the nuclear industry and concretely for the design of the reactors of the IV generation. The model is build utilizing the Proper Orthogonal Decomposition coupled with the Galerkin projection. The most energetic modes are derived from a high fidelity CFD calculation. The governing equations are henceforth projected into the manifold generated. Once the model is available, we consider uncertainties on the dimensionless numbers, Re, Pr, Ra, and on the initial conditions. The expected result and its uncertainty is computed by MonteCarlo method, calculating hundreds of solutions of the initial value problem with the surrogate model.

Tuesday, November 20, 2018 1:55PM  2:08PM 
Q32.00006: Quantifying flow uncertainty in heterogeneous porous media using random walk simulations Amir Hossein Delgoshaie, Peter W. Glynn, Patrick Jenny, Hamdi Tchelepi Elliptic and parabolic partial differential equations (PDEs) model conservation laws of many physical applications, such as heat transfer and flow in porous media. Often these PDEs have an input parameter field (conductivity) that is both heterogeneous and uncertain, and that poses significant computational challenges for quantifying the uncertainty in the flow performance. Based on the relation between stochastic diffusion processes and PDEs, Monte Carlo (MC) methods have been proposed to solve elliptic and parabolic PDEs for problems where the input conductivity field is homogeneous. However, in many practical problems with highly heterogeneous conductivity, these MC solution strategies are not directly applicable. Here, we describe a MC method to solve conservation laws with heterogeneous conductivity fields using general diffusion processes. The stochastic representation of the conservation law makes it possible to compute the solution at any point independently of the solution at other locations in the domain without solving a global linear system. It is shown that the method provides an efficient alternative for computing the statistical moments of the solution to a stochastic PDE at any point in the domain. 
Tuesday, November 20, 2018 2:08PM  2:21PM 
Q32.00007: ReducedOrder Modeling of Stochastic Bifurcation in NaturallyConvected Flows Prerna Patil, Hessam Babaee We present a reducedorder model to solve timedependent stochastic thermofluid problems with high dimensional random initial/boundary conditions. To this end, we develop a methodology for representation and evolution of spatial and stochastic modes of a random system. The flow variables are modeled as stochastic processes represented in terms of KarhunenLoeve modes. The modes dynamically evolve with the flow and adapt to the stochasticity which is introduced into the system by random initial or boundary conditions. We present our results for the Rayleigh Bernard Convection. We investigate the effect of stochastic initial conditions and stochastic boundary conditions on bifurcation. The computational performance and accuracy of this technique are compared with results from the polynomial chaos method. 
Tuesday, November 20, 2018 2:21PM  2:34PM 
Q32.00008: Investigating inflow uncertainty in LES predictions of wind loading Giacomo Lamberti, Catherine Gorle Large eddy simulations (LES) represent a powerful tool to quantify wind loads on buildings and assess wind hazards, but LES of the atmospheric boundary layer (ABL) can be strongly affected by uncertainties in the inflow conditions. We will present initial results of a sensitivity analysis to determine the importance of these inflow uncertainties when calculating wind pressure coefficients on a highrise building. The results will be validated with wind tunnel measurements. We consider 3 uncertain parameters: the ABL roughness length, turbulence kinetic energy and streamwise integral timescale. To produce incoming ABL profiles with different values for these parameters, we use a divergencefree digital filter method in combination with an optimization strategy to identify the input parameters that produce the desired ABL characteristics in the computational domain. We perform 27 LES simulations using different input parameters, and investigate their effect on the pressure distribution on the building's facade. Based on these results we will design a formal UQ approach to calculate confidence intervals for the mean, root mean square and peak pressure coefficients, and compare these results to wind tunnel measurements. 
Tuesday, November 20, 2018 2:34PM  2:47PM 
Q32.00009: Eigenspacebased sensitivity analysis of modelform uncertainty in subgridscale turbulence models Lluis Jofre, Stefan Paul Domino, Gianluca Iaccarino Largeeddy simulation (LES) has gained significant importance as a highfidelity reference technique for the resolution of complex turbulent flow. LES reduces the computational cost of solving turbulence by lowpass filtering the conservation equations. However, the effects of the small scales on the resolved flow field are not negligible, and therefore their contribution in the form of subgridscale stresses needs to be modeled. As a consequence, the assumptions introduced in the closure formulations result in potential sources of structural uncertainty that can affect the quantities of interest. Therefore, the aim of this work is to characterize their modelform uncertainty and its impact on the QoIs by means of recently developed eigenspacebased strategies. In the presentation, the strategy will be described in detail and investigations based on filtered direct numerical simulation and LES of turbulent free shear flows will be discussed. 
Tuesday, November 20, 2018 2:47PM  3:00PM 
Q32.00010: A physicsbased approach for quantifying the structural uncertainties of turbulent scalar flux models Zengrong Hao, Catherine Gorlé Turbulent scalar flux modeling is relevant to a variety of engineering problems, from heat transfer in cooling systems of buildings to urban pollutant dispersion. However, most practical models for turbulent scalar fluxes are known to fail in complex flows, and thus methods for quantifying model form uncertainties are necessary. This paper proposes a physicsbased uncertainty quantification approach for scalar flux models to estimate plausible intervals for quantities of interest related to scalar transport. The approach introduces uncertainty in the traditional model for the pressurescrambling terms in the scalar flux equation by adding an extra term with a time scale that blends the scales of turbulence and mean distortion. A nondimensional coefficient in this extra term defines the onedimensional uncertain parameter space. The approach is applied to forced heat convection simulations of a pinfin heat exchanger, and shows promising capabilities to bound the overall heat transfer rate and the Nusselt number distributions on fin and pin surfaces. 
Tuesday, November 20, 2018 3:00PM  3:13PM 
Q32.00011: Bayesian Inference for Turbulence Model Uncertainty Quantification Wouter Edeling, Aashwin Mishra, Gianluca Iaccarino Despite continued advances in highfidelity turbulent flow simulations, closure models based on 
(Author Not Attending)

Q32.00012: Design Exploration under Epistemic Uncertainties Jayant Mukhopadhaya, Aashwin Mishra, Gianluca Iaccarino, Juan Alonso Industrial design requires rapid investigation of various points in the design space. To perform these quick analyses, time intensive options such as Large Eddy Simulations (LES) or wind tunnel experiments are overlooked for the lowerfidelity, yet costeffective Reynolds Averaged NavierStokes simulations. Although useful, assumptions inherent in the turbulence models used can introduce significant modelform errors that bring into question the reliability of these results. Quantification of these uncertainties would greatly improve the ability to design robust systems. In spite of the substantial uncertainties in prediction due to turbulence models, at present, none of the available CFD software offer any utility to estimate these. In this talk, we outline the EQUiPS Module for quantifying the epistemic uncertainties due to turbulence models. This module has been tested on a variety of canonical turbulent flows, as well as complex cases relevant to aerospace and turbomachinery design. Uncertainty bounds arising from these simulations are compared to available highfidelity data. Coupled with design exploration tools, this provides a new automated approach to industrial design analysis and exploration with explicit estimation of modelform uncertainty.

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