Bulletin of the American Physical Society
70th Annual Meeting of the APS Division of Fluid Dynamics
Volume 62, Number 14
Sunday–Tuesday, November 19–21, 2017; Denver, Colorado
Session Q34: Computational Fluid Dynamics: Uncertainty QuantificationCFD
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Chair: Jorge Sousa, Stanford University Room: 102 |
Tuesday, November 21, 2017 12:50PM - 1:03PM |
Q34.00001: Non-intrusive uncertainty quantification of computational fluid dynamics simulations: notes on the accuracy and efficiency Małgorzata Zimoń, Robert Sawko, David Emerson, Christopher Thompson Uncertainty quantification (UQ) is increasingly becoming an indispensable tool for assessing the reliability of computational modelling. Efficient handling of stochastic inputs, such as boundary conditions, physical properties or geometry, increases the utility of model results significantly. We discuss the application of non-intrusive generalised polynomial chaos techniques in the context of fluid engineering simulations. Deterministic and Monte Carlo integration rules are applied to a set of problems, including ordinary differential equations and the computation of aerodynamic parameters subject to random perturbations. In particular, we analyse acoustic wave propagation in a heterogeneous medium to study the effects of mesh resolution, transients, number and variability of stochastic inputs. We consider variants of multi-level Monte Carlo and perform a novel comparison of the methods with respect to numerical and parametric errors, as well as computational cost. The results provide a comprehensive view of the necessary steps in UQ analysis and demonstrate some key features of stochastic fluid flow systems. [Preview Abstract] |
Tuesday, November 21, 2017 1:03PM - 1:16PM |
Q34.00002: Uncertainty Quantification in Multi-scale Simulations of Coronary Artery Bypass Grafts Justin Tran, Daniele Schiavazzi, Abhay Ramachandra, Andrew Kahn, Alison Marsden Hemodynamic simulations provide non-invasive descriptions of blood flow that are typically not obtainable from standard clinical imaging modalities. However, inputs parameters for such simulations are not known precisely, and uncertainty in the outputs must be quantified for reliable patient-specific predictions. Thus, this study aims to quantify the variability in computed hemodynamic indices hypothesized to correlate with coronary bypass graft failure by including uncertainties due to the model boundary conditions and material model parameters. Uncertainty in the boundary conditions is obtained by sampling parameter sets producing results consistent with uncertain clinical observations, while the effect of spatial variability in the graft material properties is modeled using random field theory. Additionally, stochastic sub-models are constructed to focus the analysis on arterial and venous grafts and to maintain a reasonable computational cost. Finally, heterogeneous inputs (either in the form of samples or with a known distribution) are propagated forward using a generalized multi-resolution stochastic expansion. Results are discussed with references to both hemodynamic indicators and wall mechanics. [Preview Abstract] |
Tuesday, November 21, 2017 1:16PM - 1:29PM |
Q34.00003: Quantifying Structural Uncertainties for Turbulent Passive Scalar Transport Zengrong Hao, Catherine Gorlé Modeling turbulent passive scalar transfer is relevant to a variety of engineering problems, such as the optimization of heat exchangers, or the prediction of pollutant dispersion in cities. Classic gradient-diffusion models for turbulent scalar flux are known to fail in complex flows, and a method to quantify model form uncertainties would provide a useful engineering tool. We therefore propose a framework for estimating the upper and lower bounds of the intensity of turbulent scalar transfer. It is based on two approximations: 1) a selected baseline turbulent scalar-flux closure is trusted in predicting the level of flux magnitude; and 2) the bounds of the scalar transfer intensity are explored by identifying local flux direction for which the local growth rate of flux magnitude reaches its maximum and minimum Accordingly, first a generalized baseline form for both transport and algebraic models of scalar-flux is suggested. Second, the growth rate of flux magnitude is represented as function of local flux direction, and the bounds are identified using an optimization for an inhomogeneous quadratic function with constraints. An algorithm for the optimization is implemented together with a damping function to avoid possible discontinuities in the flux direction field. The framework is applied to a pin-fin heat exchanger, showing promising capabilities to bound the overall heat transfer rate and some local key features. [Preview Abstract] |
Tuesday, November 21, 2017 1:29PM - 1:42PM |
Q34.00004: Eigenspace perturbations for structural uncertainty estimation of turbulence closure models Lluis Jofre, Aashwin Mishra, Gianluca Iaccarino With the present state of computational resources, a purely numerical resolution of turbulent flows encountered in engineering applications is not viable. Consequently, investigations into turbulence rely on various degrees of modeling. Archetypal amongst these variable resolution approaches would be RANS models in two-equation closures, and subgrid-scale models in LES. However, owing to the simplifications introduced during model formulation, the fidelity of all such models is limited, and therefore the explicit quantification of the predictive uncertainty is essential. In such scenario, the ideal uncertainty estimation procedure must be agnostic to modeling resolution, methodology, and the nature or level of the model filter. The procedure should be able to give reliable prediction intervals for different Quantities of Interest, over varied flows and flow conditions, and at diametric levels of modeling resolution. In this talk, we present and substantiate the Eigenspace perturbation framework as an uncertainty estimation paradigm that meets these criteria. Commencing from a broad overview, we outline the details of this framework at different modeling resolution. Thence, using benchmark flows, along with engineering problems, the efficacy of this procedure is established. [Preview Abstract] |
Tuesday, November 21, 2017 1:42PM - 1:55PM |
Q34.00005: Uncertainty Quantification for Combined Polynomial Chaos Kriging Surrogate Models Justin Weinmeister, Xinfeng Gao, Aditi Krishna Prasad, Sourajeet Roy Surrogate modeling techniques are currently used to perform uncertainty quantification on computational fluid dynamics (CFD) models for their ability to identify the most impactful parameters on CFD simulations and help reduce computational cost in engineering design process. The accuracy of these surrogate models depends on a number of factors, such as the training data created from the CFD simulations, the target functions, the surrogate model framework, and so on. Recently, we have combined polynomial chaos expansions (PCE) and Kriging to produce a more accurate surrogate model, polynomial chaos Kriging (PCK). In this talk, we analyze the error convergence rate for the Kriging, PCE, and PCK model on a convection-diffusion-reaction problem, and validate the statistical measures and performance of the PCK method for its application to practical CFD simulations. [Preview Abstract] |
Tuesday, November 21, 2017 1:55PM - 2:08PM |
Q34.00006: Inadequacy representation of flamelet-based RANS model for turbulent non-premixed flame Myoungkyu Lee, Todd Oliver, Robert Moser Stochastic representations for model inadequacy in RANS-based models of non-premixed jet flames are developed and explored. Flamelet-based RANS models are attractive for engineering applications relative to higher-fidelity methods because of their low computational costs. However, the various assumptions inherent in such models introduce errors that can significantly affect the accuracy of computed quantities of interest. In this work, we develop an approach to represent the model inadequacy of the flamelet-based RANS model. In particular, we pose a physics-based, stochastic PDE for the triple correlation of the mixture fraction. This additional uncertain state variable is then used to construct perturbations of the PDF for the instantaneous mixture fraction, which is used to obtain an uncertain perturbation of the flame temperature. A hydrogen-air non-premixed jet flame is used to demonstrate the representation of the inadequacy of the flamelet-based RANS model. [Preview Abstract] |
Tuesday, November 21, 2017 2:08PM - 2:21PM |
Q34.00007: Uncertainty quantification in Eulerian-Lagrangian models for particle-laden flows Vasileios Fountoulakis, Gustaaf Jacobs, HS Udaykumar A common approach to ameliorate the computational burden in simulations of particle-laden flows is to use a point-particle based Eulerian-Lagrangian model, which traces individual particles in their Lagrangian frame and models particles as mathematical points. The particle motion is determined by Stokes drag law, which is empirically corrected for Reynolds number, Mach number and other parameters. The empirical corrections are subject to uncertainty. Treating them as random variables renders the coupled system of PDEs and ODEs stochastic. An approach to quantify the propagation of this parametric uncertainty to the particle solution variables is proposed. The approach is based on averaging of the governing equations and allows for estimation of the first moments of the quantities of interest. We demonstrate the feasibility of our proposed methodology of uncertainty quantification of particle-laden flows on one-dimensional linear and nonlinear Eulerian-Lagrangian systems. [Preview Abstract] |
Tuesday, November 21, 2017 2:21PM - 2:34PM |
Q34.00008: Simulation of noisy dynamical system by Deep Learning Kyongmin Yeo Deep learning has attracted huge attention due to its powerful representation capability. However, most of the studies on deep learning have been focused on visual analytics or language modeling and the capability of the deep learning in modeling dynamical systems is not well understood. In this study, we use a recurrent neural network to model noisy nonlinear dynamical systems. In particular, we use a long short-term memory (LSTM) network, which constructs internal nonlinear dynamics systems. We propose a cross-entropy loss with spatial ridge regularization to learn a non-stationary conditional probability distribution from a noisy nonlinear dynamical system. A Monte Carlo procedure to perform time-marching simulations by using the LSTM is presented. The behavior of the LSTM is studied by using noisy, forced Van der Pol oscillator and Ikeda equation. [Preview Abstract] |
Tuesday, November 21, 2017 2:34PM - 2:47PM |
Q34.00009: Machine Learning Algorithms for prediction of regions of high Reynolds Averaged Navier Stokes Uncertainty Aashwin Mishra, Gianluca Iaccarino In spite of their deficiencies, RANS models represent the workhorse for industrial investigations into turbulent flows. In this context, it is essential to provide diagnostic measures to assess the quality of RANS predictions. To this end, the primary step is to identify feature importances amongst massive sets of potentially descriptive and discriminative flow features. This aids the physical interpretability of the resultant discrepancy model and its extensibility to similar problems. Recent investigations have utilized approaches such as Random Forests, Support Vector Machines and the Least Absolute Shrinkage and Selection Operator for feature selection. With examples, we exhibit how such methods may not be suitable for turbulent flow datasets. The underlying rationale, such as the correlation bias and the required conditions for the success of penalized algorithms, are discussed with illustrative examples. Finally, we provide alternate approaches using convex combinations of regularized regression approaches and randomized sub-sampling in combination with feature selection algorithms, to infer model structure from data. [Preview Abstract] |
Tuesday, November 21, 2017 2:47PM - 3:00PM |
Q34.00010: Estimating the State of Aerodynamic Flows in the Presence of Modeling Errors Andre F. C. da Silva, Tim Colonius The ensemble Kalman filter (EnKF) has been proven to be successful in fields such as meteorology, in which high-dimensional nonlinear systems render classical estimation techniques impractical. When the model used to forecast state evolution misrepresents important aspects of the true dynamics, estimator performance may degrade. In this work, parametrization and state augmentation are used to track misspecified boundary conditions (e.g., free stream perturbations). The resolution error is modeled as a Gaussian-distributed random variable with the mean (bias) and variance to be determined. The dynamics of the flow past a NACA 0009 airfoil at high angles of attack and moderate Reynolds number is represented by a Navier-Stokes equations solver with immersed boundaries capabilities. The pressure distribution on the airfoil or the velocity field in the wake, both randomized by synthetic noise, are sampled as measurement data and incorporated into the estimated state and bias following Kalman's analysis scheme. Insights about how to specify the modeling error covariance matrix and its impact on the estimator performance are conveyed. [Preview Abstract] |
Tuesday, November 21, 2017 3:00PM - 3:13PM |
Q34.00011: Data-free and data-driven spectral perturbations for RANS UQ Wouter Edeling, Aashwin Mishra, Gianluca Iaccarino Despite recent developments in high-fidelity turbulent flow simulations, RANS modeling is still vastly used by industry, due to its inherent low cost. Since accuracy is a concern in RANS modeling, model-form UQ is an essential tool for assessing the impacts of this uncertainty on quantities of interest. Applying the spectral decomposition to the modeled Reynolds-Stress Tensor (RST) allows for the introduction of decoupled perturbations into the baseline intensity (kinetic energy), shape (eigenvalues), and orientation (eigenvectors). This constitutes a natural methodology to evaluate the model form uncertainty associated to different aspects of RST modeling. In a predictive setting, one frequently encounters an absence of any relevant reference data. To make data-free predictions with quantified uncertainty we employ physical bounds to a-priori define maximum spectral perturbations. When propagated, these perturbations yield intervals of engineering utility. High-fidelity data opens up the possibility of inferring a distribution of uncertainty, by means of various data-driven machine-learning techniques. We will demonstrate our framework on a number of flow problems where RANS models are prone to failure. [Preview Abstract] |
Tuesday, November 21, 2017 3:13PM - 3:26PM |
Q34.00012: Vortex-based flow estimation with an ensemble Kalman filter Darwin Darakananda, Jeff D. Eldredge, Andre Fernando de Castro da Silva, Tim Colonius Inviscid vortex models have been used for decades to investigate unsteady aerodynamics, including those with leading-edge separation. While these models successfully capture the qualitative behavior of the force response at large angles, the lack of a leading-edge condition makes them poor predictors of separated flows, and the buildup of vortex particles renders them increasingly inefficient over time. In this work, we introduce a flow estimator based on the Ensemble Kalman Filter, in which the prediction of an ensemble of inviscid vortex models is improved by incorporating surface pressure measurements from an experiment. Our state consists of the position and circulation of all the vortex particles, as well as critical suction parameters that govern vortex shedding from the two edges of the airfoil. To prevent the dimension of the state from continuously increasing over time, we introduce a vortex pruning algorithm that regularly merges dynamically related clusters of vortex particles. We demonstrate the estimator on a variety of problems, including pitch-up, impulsive translation, as well as flows with pulse actuation near the leading edge. [Preview Abstract] |
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