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 A31: Computational Fluid Dynamics: ReducedOrder and MultiFidelity ModelingCFD

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Chair: Aashwin Mishra, Center for Turbulence Research, Stanford University Room: 108 
Sunday, November 19, 2017 8:00AM  8:13AM 
A31.00001: MultiFidelity Uncertainty Propagation for Cardiovascular Modeling Casey Fleeter, Gianluca Geraci, Daniele Schiavazzi, Andrew Kahn, Alison Marsden Hemodynamic models are successfully employed in the diagnosis and treatment of cardiovascular disease with increasing frequency. However, their widespread adoption is hindered by our inability to account for uncertainty stemming from multiple sources, including boundary conditions, vessel material properties, and model geometry. In this study, we propose a stochastic framework which leverages three cardiovascular model fidelities: 3D, 1D and 0D models. 3D models are generated from patientspecific medical imaging (CT and MRI) of aortic and coronary anatomies using the SimVascular opensource platform, with fluid structure interaction simulations and Windkessel boundary conditions. 1D models consist of a simplified geometry automatically extracted from the 3D model, while 0D models are obtained from equivalent circuit representations of blood flow in deformable vessels. Multilevel and multifidelity estimators from Sandia's opensource DAKOTA toolkit are leveraged to reduce the variance in our estimated output quantities of interest while maintaining a reasonable computational cost. The performance of these estimators in terms of computational cost reductions is investigated for a variety of output quantities of interest, including global and local hemodynamic indicators. [Preview Abstract] 
Sunday, November 19, 2017 8:13AM  8:26AM 
A31.00002: Multifidelity uncertainty quantification in largescale predictive simulations of turbulent flow Gianluca Geraci, Lluis JofreCruanyes, Gianluca Iaccarino The performance characterization of complex engineering systems often relies on accurate, but computationally intensive numerical simulations. It is also well recognized that in order to obtain a reliable numerical prediction the propagation of uncertainties needs to be included. Therefore, Uncertainty Quantification (UQ) plays a fundamental role in building confidence in predictive science. Despite the great improvement in recent years, even the more advanced UQ algorithms are still limited to fairly simplified applications and only moderate parameter dimensionality. Moreover, in the case of extremely large dimensionality, sampling methods, i.e. Monte Carlo (MC) based approaches, appear to be the only viable alternative. In this talk we describe and compare a family of approaches which aim to accelerate the convergence of standard MC simulations. These methods are based on hierarchies of generalized numerical resolutions (multilevel) or model fidelities (multifidelity), and attempt to leverage the correlation between Low and HighFidelity (HF) models to obtain a more accurate statistical estimator without introducing additional HF realizations. The performance of these methods are assessed on an irradiated particle laden turbulent flow (PSAAP II solar energy receiver). [Preview Abstract] 
Sunday, November 19, 2017 8:26AM  8:39AM 
A31.00003: A MultiFidelity Surrogate Model for the Equation of State for Mixtures of Real Gases Frederick Ouellet, Chanyoung Park, Rahul Koneru, S. Balachandar, Bertrand Rollin The explosive dispersal of particles is a complex multiphase and multispecies fluid flow problem. In these flows, the products of detonated explosives must be treated as real gases while the ideal gas equation of state is used for the ambient air. As the products expand outward, they mix with the air and create a region where both state equations must be satisfied. One of the most accurate, yet expensive, methods to handle this problem is an algorithm that iterates between both state equations until both pressure and thermal equilibrium are achieved inside of each computational cell. This work creates a multifidelity surrogate model to replace this process. This is achieved by using a Kriging model to produce a curve fit which interpolates selected data from the iterative algorithm. The surrogate is optimized for computing speed and model accuracy by varying the number of sampling points chosen to construct the model. The performance of the surrogate with respect to the iterative method is tested in simulations using a finite volume code. The model's computational speed and accuracy are analyzed to show the benefits of this novel approach. [Preview Abstract] 
Sunday, November 19, 2017 8:39AM  8:52AM 
A31.00004: Basis Reduction for Uncertainty Quantification  A Bifidelity Approach Felix Newberry, Michaela Farr, Alireza Doostan Minimization of computational cost is a ubiquitous challenge in uncertainty quantification or design space exploration of fluid mechanics simulations. A useful tool to ease the burden of solving complex systems of PDEs, which arise in such simulations, is model reduction. We present a stochastic basis reduction method in which lowfidelity samples are employed to inform the construction of a reduced basis. Approximating the highfidelity quantities of interest in this reduced basis requires a small number of highfidelity samples to achieve a bifidelity estimate. The premise of this approach is that while a lowfidelity model may be inaccurate in terms of predicting the quantities of interest, it will represent the stochastic space of the problem for an accurate bifidelity approximation. We then present the successful application of this algorithm in two scenarios: a lid driven cavity and an airfoil. In both cases we achieve acceptable errors for a minimal number of highfidelity model evaluations. [Preview Abstract] 
Sunday, November 19, 2017 8:52AM  9:05AM 
A31.00005: Unbiased multifidelity estimate of failure probability of a free plane jet Alexandre Marques, Boris Kramer, Karen Willcox, Benjamin Peherstorfer Estimating failure probability related to fluid flows is a challenge because it requires a large number of evaluations of expensive models. We address this challenge by leveraging multiple low fidelity models of the flow dynamics to create an optimal unbiased estimator. In particular, we investigate the effects of uncertain inlet conditions in the width of a free plane jet. We classify a condition as failure when the corresponding jet width is below a small threshold, such that failure is a rare event (failure probability is smaller than 0.001). We estimate failure probability by combining the frameworks of multifidelity importance sampling and optimal fusion of estimators. Multifidelity importance sampling uses a low fidelity model to explore the parameter space and create a biasing distribution. An unbiased estimate is then computed with a relatively small number of evaluations of the high fidelity model. In the presence of multiple low fidelity models, this framework offers multiple competing estimators. Optimal fusion combines all competing estimators into a single estimator with minimal variance. We show that this combined framework can significantly reduce the cost of estimating failure probabilities, and thus can have a large impact in fluid flow applications. [Preview Abstract] 
Sunday, November 19, 2017 9:05AM  9:18AM 
A31.00006: Low Dimensional Study of a Supersonic MultiStream Jet Flow Andrew Tenney, Matthew Berry, Halley AycockRizzo, Mark Glauser, Jacques Lewalle In this study, the near field of a two stream supersonic jet flow is examined using low dimensional tools. The flow issues from a multistream nozzle as described in \textit{A nearfield investigation of a supersonic, multistream jet: locating turbulence mechanisms through velocity and density measurements} by Magstadt at el., with the bulk flow Mach number, M$_{\mathrm{1}}$, being 1.6, and the second stream Mach number, M$_{\mathrm{2}}$, reaching the sonic condition. The flow field is visualized using Particle Image Velocimetry (PIV), with frames captured at a rate of 4Hz. Timeresolved pressure measurements are made just aft of the nozzle exit, as well as in the farfield, 86.6 nozzle hydraulic diameters away from the exit plane. The methodologies used in the analysis of this flow include Proper Orthogonal Decomposition (POD), and the continuous wavelet transform. The results from this ``no deck'' case are then compared to those found in the study conducted by Berry et al. From this comparison, we draw conclusions about the effects of the presence of an aft deck on the low dimensional flow description, and near field spectral content. [Preview Abstract] 
Sunday, November 19, 2017 9:18AM  9:31AM 
A31.00007: A DataDriven LowRank Approximation of TimeDependent Stochastic Flows Hessam Babaee We present a nonintrusive and datadriven method for constructing a lowrank approximation of timedependent stochastic flows. This method requires a snapshot sequence of samples of the stochastic field in the form of $\mathbf{A} \in \mathbb{R}^{n\times s \times m}$ where $n$ is the number of observable data points, $s$ is the number of samples and $m$ is the number time steps. These samples may be generated using deterministic solvers or timeresolved PIV experimental measurements. In this methodology, the timedependent data is approximated by an $r$dimensional reduction in the form of: $\mathbf{A}^r(t)= \mathbf{U}(t) \mathbf{Y}(t)^T $ where $\mathbf{U}(t) \in \mathbb{R}^{n\times r}$ is a set of deterministic timedependent orthonormal basis and $\mathbf{Y}(t) \in \mathbb{R}^{s\times r}$ are the stochastic coefficients. We derive explicit evolution equations for $\mathbf{U}(t)$ and $\mathbf{Y}(t)$ and use the data to solve these equations. We demonstrate that this reduction technique captures the strongly transient stochastic flows with highdimensional random dimensions. We present the capability of this method for two classical fluid dynamics problems: (1) flow over a cylinder, and (2) threedimensional jet in a crossflow. [Preview Abstract] 
Sunday, November 19, 2017 9:31AM  9:44AM 
A31.00008: Creating Turbulent Flow Realizations with Generative Adversarial Networks Ryan King, Peter Graf, Michael Chertkov Generating valid inflow conditions is a crucial, yet computationally expensive, step in unsteady turbulent flow simulations. We demonstrate a new technique for rapid generation of turbulent inflow realizations that leverages recent advances in machine learning for image generation using a deep convolutional generative adversarial network (DCGAN). The DCGAN is an unsupervised machine learning technique consisting of two competing neural networks that are trained against each other using backpropagation. One network, the generator, tries to produce samples from the true distribution of states, while the discriminator tries to distinguish between true and synthetic samples. We present results from a fullytrained DCGAN that is able to rapidly draw random samples from the full distribution of possible inflow states without needing to solve the NavierStokes equations, eliminating the costly process of spinning up inflow turbulence. This suggests a new paradigm in physics informed machine learning where the turbulence physics can be encoded in either the discriminator or generator. Finally, we also propose additional applications such as feature identification and subgrid scale modeling. [Preview Abstract] 
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