Bulletin of the American Physical Society
67th Annual Meeting of the APS Division of Fluid Dynamics
Volume 59, Number 20
Sunday–Tuesday, November 23–25, 2014; San Francisco, California
Session M31: CFD: Uncertainty Quantification |
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Chair: Onkar Sahni, Rensselaer Polytechnic Institute Room: 2018 |
Tuesday, November 25, 2014 8:00AM - 8:13AM |
M31.00001: Statistical analysis and simulation of random shock waves in scalar conservation laws Daniele Venturi, Heyrim Cho, George Karniadakis Hyperbolic conservation laws subject to additive random noise and random initial conditions can develop random shock waves at random space-time locations. The statistical analysis of such waves is quite complex, due to non-linearities, high-dimensionality and lack of regularity. By using the Mori-Zwanzig formulation of irreversible statistical mechanics, we derive formally exact reduced-order equations for the one- and two-point probability density function of the solution field. This allows us to perform numerical simulations and determine the statistical properties of the system. We consider the inviscid limit of the stochastic Burgers equation as a model problem and determine its solution in physical and probability spaces by using adaptive discontinuous Galerkin methods. In particular, we study stochastic flows generated by random initial states and random additive noise, yielding multiple interacting shock waves collapsing into clusters and settling down to a similarity state. We also address the question of how random shock waves in space and time manifest themselves in probability space. The mathematical framework is general and it can be applied to other systems, leading to new insights in high-dimensional stochastic dynamics and more efficient computational algorithms. [Preview Abstract] |
Tuesday, November 25, 2014 8:13AM - 8:26AM |
M31.00002: Quantification of the uncertainty of finite-time-average approximations of infinite-time-average statistics in turbulence simulations Pooriya Beyhaghi, Thomas Bewley Turbulent flows are often stationary and ergodic, which means that the time average of a quantity (TKE, total drag, etc) converges to a constant as the averaging interval is increased. This infinite-time-averaged statistic is of particular interest in many problems, such as aerodynamic shape optimization. Since taking an average over an infinite time horizon is not possible in simulation, some finite-time approximation of the infinite-time-average statistic of interest is generally used in practice. The error of this approximation decreases slowly, like the reciprocal of the square roots of the averaging time. In the present work, we develop a framework to quantify precisely the uncertainty of such a finite-time-average approximation of an infinite-time-average statistic of a stationary ergodic process. In the method used, different statistical models for stationary processes have been examined to model the statistical behavior of the time series derived from the turbulence simulation. It is observed that the statistical behavior of some of these models is sufficiently representative of that of the real time series that they provide an accurate estimate of the uncertainty associated with the finite time average approximation of the statistic of interest. [Preview Abstract] |
Tuesday, November 25, 2014 8:26AM - 8:39AM |
M31.00003: Uncertainty Quantification of RANS dispersion modeling in Oklahoma City during the Joint Urban 2003 campaign Clara Garcia-Sanchez, Catherine Gorle, Jeroen Van Beeck, Gianluca Iaccarino The high expansion rate of urban areas makes realistic predictions of dispersion within cities an important research topic. The transport of pollutants is influenced by wind flows that are affected by the large scale variability of the atmospheric boundary layer (ABL). In order to improve the predictive capabilities of Computational Fluid Dynamics simulations (CFD) of the ABL, this atmospheric variability should be included. This work focuses on representing this variability in the inflow boundary conditions using an uncertainty quantification framework for the Joint Urban 2003 experiment. The simulations focus on the Intensive Observation Period number 9, where a continuous release of SF6 took place in downtown Oklahoma. The RANS simulations with the k-epsilon turbulence model were performed with the code OpenFOAM, and an equation for passive scalar transport is solved, using a standard gradient diffusion model for the turbulent dispersion, to obtain the SF6 concentration. To define the inflow boundary conditions three uncertain parameters are used: wind speed, wind direction, and ABL roughness height. To propagate these uncertainties a tensor grid Clenshaw-Curtis Stochastic Collocation approach was used, and a polynomial chaos representation of the velocity and concentration at different field measurement locations was constructed to extract the mean and standard deviations. [Preview Abstract] |
Tuesday, November 25, 2014 8:39AM - 8:52AM |
M31.00004: Statistically accurate low-order models for uncertainty quantification in turbulent dynamical systems Themistoklis Sapsis A framework for low-order predictive statistical modeling and uncertainty quantification in turbulent dynamical systems will be presented. These reduced-order, modified quasilinear Gaussian (ROMQG) algorithms apply to turbulent dynamical systems in which there is significant linear instability or linear non-normal dynamics in the unperturbed system and energy-conserving non-linear interactions that transfer energy from the unstable modes to the stable modes where dissipation occurs, resulting in a statistical steady state; such turbulent dynamical systems are ubiquitous in geophysical and engineering turbulence. The ROMQG method involves constructing a low-order, nonlinear, dynamical system for the mean and covariance statistics in the reduced subspace that has the unperturbed statistics as a stable fixed point and optimally incorporates the indirect effect of non-Gaussian third-order statistics for the unperturbed system in a systematic calibration stage. This calibration procedure is achieved through information involving only the mean and covariance statistics for the unperturbed equilibrium. The performance of the ROMQG algorithm is assessed on two stringent test cases: the 40-mode Lorenz 96 model mimicking midlatitude atmospheric turbulence and two-layer baroclinic models for high-latitude ocean turbulence with over 125,000 degrees of freedom. [Preview Abstract] |
Tuesday, November 25, 2014 8:52AM - 9:05AM |
M31.00005: Toward Uncertainty Quantification of Turbulence Closure Models Aashwin Mishra, Sharath Girimaji Predictive turbulence calculations require that the uncertainty in various constituent closures is quantified. We propose that uncertainty quantification must commence at the Reynolds stress closure level, specifically, with the pressure-strain correlation term. The Reynolds stress tensor provides an insufficient basis to describe the internal structure of a turbulent field, expressly its dimensionality. It is demonstrated that this leads to an inherent degree of uncertainty in classical models for turbulent flows. Using Interval Analysis, we quantify the propagation of this epistemic uncertainty for rapid pressure strain correlation models for different regimes of mean flow. It is exhibited that the magnitude of this uncertainty is dependent not just upon the dimensionality of the turbulent field, but to a greater degree upon the nature of the mean flow. In contrast to prior beliefs, we prove that such uncertainty is present (and even greater) in the absence of mean rotation. Finally, we analyze the qualitative and quantitative effects of the non-linear component of pressure on this systemic uncertainty. [Preview Abstract] |
Tuesday, November 25, 2014 9:05AM - 9:18AM |
M31.00006: Stochastic modeling of jet in crossflow using dynamically orthogonal decomposition Hessam Babaee, Themistoklis Sapsis, George Karniadakis In this numerical study the effect of stochastic perturbation on jet in crossflow is investigated. To efficiently quantify the evolution of stochasticity in such a system, the dynamically orthogonal method is used. In this methodology, the solution is approximated by a \textit{generalized} Karhunen-Loeve (KL) expansion in the form of ${\rm {\bf u}}({\rm {\bf x}},t;\omega )=\overline {{\rm {\bf u}}} ({\rm {\bf x}},t)+\sum\nolimits_{i=1}^N {\rm {\bf y}}_{i} (t;\omega ){\rm {\bf u}}_{i} ({\rm {\bf x}},t)$, in which $\overline {{\rm {\bf u}}} ({\rm {\bf x}},t)$ is the stochastic mean, the set of ${\rm {\bf u}}_{i} ({\rm {\bf x}},t)$'s is a deterministic orthogonal basis and ${\rm {\bf y}}_{i} (t;\omega )$'s are the stochastic coefficients. Explicit evolution equations for $\overline {{\rm {\bf u}}} $, ${\rm {\bf u}}_{i} $ and ${\rm {\bf y}}_{i} $ are formulated. The elements of the basis ${\rm {\bf u}}_{i} ({\rm {\bf x}},t)$'s remain orthogonal for all times and they evolve according to the system dynamics to capture the energetically dominant stochastic subspace. In this study, the stochasticity is introduced at the crossflow boundary condition and, in particular, the effect of different time and length scales of the stochastic perturbation on the jet dynamics is investigated. The energy cascades and correlation between stochastic energy levels in the statistical sense are also analyzed. The relationship between the dynamic stochastic modes and the coherent structures present in jet in crossflow is discussed. [Preview Abstract] |
Tuesday, November 25, 2014 9:18AM - 9:31AM |
M31.00007: Representing Model Inadequacy in Combustion Kinetics Rebecca E. Morrison, Robert D. Moser An accurate description of the chemical processes involved in the oxidation of hydrocarbons may include hundreds of reactions and thirty or more chemical species. Kinetics models of these chemical mechanisms are often embedded in a fluid dynamics solver to represent combustion. Because the computational cost of such detailed mechanisms is so high, it is common practice to use drastically reduced mechanisms. But, this introduces modeling errors which may render the model inadequate. In this talk, we present a formulation of the model inadequacy in reduced models of hydrogen combustion. Our goal is to account for the discrepancy between the high-fidelity model and its reduced version by incorporating an additive, linear, probabilistic inadequacy model. In effect, it is a random matrix, whose entries are characterized by probability distributions and which displays interesting properties due to conservation constraints. The distributions are calibrated via Bayesian inference using a hierarchical modeling scheme and high-dimensional MCMC. We apply this technique to a stand-alone reaction and also incorporate it within a one-dimensional laminar flame problem. [Preview Abstract] |
Tuesday, November 25, 2014 9:31AM - 9:44AM |
M31.00008: Adaptive Discrete Equation Method for injection of stochastic cavitating flows Gianluca Geraci, Maria Giovanna Rodio, Gianluca Iaccarino, Remi Abgrall, Pietro Congedo This work aims at the improvement of the prediction and of the control of biofuel injection for combustion. In fact, common injector should be optimized according to the specific physical/chemical properties of biofuels. In order to attain this scope, an optimized model for reproducing the injection for several biofuel blends will be considered. The originality of this approach is twofold, i) the use of cavitating two-phase compressible models, known as Baer \& Nunziato, in order to reproduce the injection, and ii) the design of a global scheme for directly taking into account experimental measurements uncertainties in the simulation. In particular, stochastic intrusive methods display a high efficiency when dealing with discontinuities in unsteady compressible flows. We have recently formulated a new scheme for simulating stochastic multiphase flows relying on the Discrete Equation Method (DEM) for describing multiphase effects. The set-up of the intrusive stochastic method for multiphase unsteady compressible flows in quasi 1D configuration will be presented. The target test-case is a multiphase unsteady nozzle for injection of biofuels, described by complex thermodynamics models, for which experimental data and associated uncertainties are available. [Preview Abstract] |
Tuesday, November 25, 2014 9:44AM - 9:57AM |
M31.00009: Regression-based adaptive sparse polynomial dimensional decomposition for sensitivity analysis Kunkun Tang, Pietro Congedo, Remi Abgrall Polynomial dimensional decomposition (PDD) is employed in this work for global sensitivity analysis and uncertainty quantification of stochastic systems subject to a large number of random input variables. Due to the intimate structure between PDD and Analysis-of-Variance, PDD is able to provide simpler and more direct evaluation of the Sobol' sensitivity indices, when compared to polynomial chaos (PC). Unfortunately, the number of PDD terms grows exponentially with respect to the size of the input random vector, which makes the computational cost of the standard method unaffordable for real engineering applications. In order to address this problem of curse of dimensionality, this work proposes a variance-based adaptive strategy aiming to build a cheap meta-model by sparse-PDD with PDD coefficients computed by regression. During this adaptive procedure, the model representation by PDD only contains few terms, so that the cost to resolve repeatedly the linear system of the least-square regression problem is negligible. The size of the final sparse-PDD representation is much smaller than the full PDD, since only significant terms are eventually retained. Consequently, a much less number of calls to the deterministic model is required to compute the final PDD coefficients. [Preview Abstract] |
Tuesday, November 25, 2014 9:57AM - 10:10AM |
M31.00010: Model Calibration and Forward Uncertainty Quantification for Large-Eddy Simulation of Turbulent Flows Cosmin Safta, Myra Blaylock, Jeremy Templeton, Stefan Domino Large Eddy Simulation (LES) has the potential to significantly impact the engineering design process, but requires model calibration and error estimation for appropriate simulations to be affordable on the design time-scale. In this study we highlight a Bayesian calibration approach followed by a forward uncertainty quantification study for LES. First, we employ forced isotropic turbulence data from the Johns Hopkins Turbulence Database to calibrate parameters for a subgrid scale turbulence kinetic energy model. We discuss the effects of filter size, prior information, and error models on the posterior probability densities of model parameters. These densities are then propagated forward through LES of canonical channel flow to obtain probability densities for several Quantities of Interest (QoI). For this study we employ non-intrusive Polynomial Chaos expansion techniques for an efficient propagation of uncertainties from input model parameters to output QoI resulted from LES of channel flow. [Preview Abstract] |
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