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 A01: Nonlinear Dynamics: Model Reduction I |
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Chair: Daniel Bodony, University of Illinois Urbana-Champaign Room: Georgia World Congress Center B201 |
Sunday, November 18, 2018 8:00AM - 8:13AM |
A01.00001: The Use of Approximate Inertial Manifolds for Chaotic Systems including Turbulent Flows Maryam Akram, Malik Hassanaly, Venkatramanan Raman While much of turbulence modeling focuses on the statistical approach, a dynamical systems perspective provides useful insights that can enable more accurate representation of the small-scale features. For an ergodic system, the turbulent flow can be assumed to prescribe an inertial manifold. An IM is defined as a finite-dimensional positively invariant Lipschitz manifold which exponentially attracts all trajectories and contains the global attractor. The existence of IM has been proven for many systems described by dissipative PDE; however, the theory does not provide an explicit form for the IM of such systems. Thus, to describe dynamical systems in inertial form, an approximation is necessary. When a suitable projection operator is used to split the full state of the system into resolved and unresolved scales, it is possible to develop such an approximation, and this has been demonstrated elsewhere for canonical chaotic systems. In this work, this approximate inertial manidfold method is tested for a series of canonical flows and applied to homogeneous isotropic turbulence. |
Sunday, November 18, 2018 8:13AM - 8:26AM |
A01.00002: Low-Rank Modeling of Primary Atomization Daniel Joseph Bodony, Palash Sashittal Improving primary atomization of a liquid jet in a gas environment by active control can potentially benefit several engineering systems. We propose a low-rank method to reconstruct and predict the multiphase field from time histories of volume-of-fluid data. The method combines elements from image processing, dynamic mode decomposition, and optical flow to form a low-rank model that can retain a sharp interface with complex topological features, like ligaments and drops. The method is applied to volume-of-fluid data acquired from the simulation of the primary atomization of a water jet and used to develop a reduce-order controller to improve the jet's atomization. |
Sunday, November 18, 2018 8:26AM - 8:39AM |
A01.00003: Symmetries, Dynamics, and Control of a Seventh-Order Reduced ODE System of the 2-d Navier-Stokes Equations Nejib Smaoui The symmetries, dynamics and control problem of the two dimensional (2-d) Navier-Stokes (N-S) equations with periodic boundary conditions and with a forcing in the mode (0, 2) known as 2-d Kolmogorov flow are addressed. First, using the Fourier Galerkin method, we obtain a seventh order system of nonlinear ordinary differential equations (ODE) which approximates the behavior of the Kolmogorov flow. The dynamics and symmetries of the reduced seventh-order system are analyzed through computer simulations. Extensive numerical simulations show that the obtained system is able to display different behaviors of the Kolmogorov flow. Then, Lyapunov based controllers are designed to control the dynamics of the system of ODEs to different attractors (e.g., a fixed point, a periodic orbit or a chaotic attractor). Finally, numerical simulations are undertaken to validate the theoretical developments. |
Sunday, November 18, 2018 8:39AM - 8:52AM |
A01.00004: Spectral representation and filtering of incompressible flow Siavash Ameli, Sarah Frank, Shawn C Shadden Several approaches exist to functionally project fluid velocity field data; proper orthogonal decomposition, dynamic mode decomposition, radial basis functions and smoothing kernels, spectral filtering by Fourier representation and wavelet transforms are a few examples. Often this projection is done to de-noise or filter measured velocity field data, yet for many applications the necessity of an incompressible projection is important. In this talk, we present a spectral representation of multi-dimensional vector fields that directly addresses incompressibility. The spectral representation of the fluid flow is obtained by the Galerkin projection of the flow to a class of solenoidal and orthogonal eigenmodes that satisfy the flow boundary conditions. We demonstrate that these eigenmodes span the functional space of solenoidal vector fields. Using these modes, flow field data can be filtered using a truncated series of modes where incompressibility and boundary conditions are preserved. We provide the upper bound of the approximation error and convergence rate, and demonstrate results using example data. |
Sunday, November 18, 2018 8:52AM - 9:05AM |
A01.00005: One-dimensional phase-reduction analysis for identifying wake lock-on characteristics Kunihiko Taira, Chi-An Yeh, Hiroya Nakao Characterization of lock-on for periodic wake flows generally requires an extensive parametric study through experiments or simulations. We instead examine lock-on (phase synchronization) by reducing the high-dimensional wake dynamics into its one-dimensional phase dynamics. We define the phase through a sensor measurement and reveal the phase sensitivity against perturbations. With the phase sensitivity function characterized, we are able to take a convolution of this function with a chosen periodic external forcing to determine its effect of lock on. This approach reveals the phase synchronization properties of the flow, including the Arnold tongue over the perturbation frequency and amplitude. Here, we apply the phase-reduction analysis to determine the lock-on characteristics of bluff-body wakes for active flow control and unsteady body maneuvers. This one-dimensional analysis can be performed in experiments and simulations, offering a pathway to examine how unsteady periodic flows responds to external forcing. |
Sunday, November 18, 2018 9:05AM - 9:18AM |
A01.00006: Enabling predictive reduced order modeling of high-fidelity wind plant simulations with in-situ modal decomposition and basis interpolation Ryan King, Jennifer Annoni, Alireza Doostan, Michael Alan Sprague As wind plant simulation capabilities approach exascale, new challenges emerge regarding reduced order models (ROM) for realtime controls, uncertainty quantification, and data compression. Exascale paradigms favor ROM techniques that minimize storage and communication in a distributed environment. Many reduced order modeling and machine learning techniques require a decomposition of a snapshot matrix that is prohibitively expensive to store and access in exascale simulations. To overcome this barrier, we demonstrate a single-pass randomized SVD of high fidelity wind plant simulations that minimizes storage and communication requirements. These matrix factorizations are used to develop a linear parameter-varying dynamic mode decomposition model that can smoothly interpolate the reduced order model to unseen inflows. A key challenge for these systems is determining linearizations at new operating points. We compare two possible approaches for obtaining new linearizations: local basis interpolation on Stieffel manifolds, and using a lower fidelity analytical model. These developments enable truly predictive ROM’s for exascale simulation capabilities. |
Sunday, November 18, 2018 9:18AM - 9:31AM |
A01.00007: Greedy Sensor and Actuator Placement Using Balanced Model Reduction Krithika Manohar, J. Nathan Kutz, Steven L Brunton Optimal sensor and actuator placement is one of the foremost challenges in the estimation and control of high-dimensional complex systems. For high-dimensional systems it is impractical to monitor or actuate every state, and the determination of a few optimal sensors and actuators amounts to a brute-force combinatorial search across all possible placements. In this work, we exploit balanced model reduction to efficiently determine sensor and actuator placements to maximize the observability and controllability of the reduced system. In particular, we choose sensors and actuators that maximize the volume of the associated observability and controllability ellipsoids in the balanced transform coordinates. The placements are then determined using a greedy matrix pivoting algorithm on the direct and adjoint balancing modes. The pivoting procedure scales linearly with the state dimension, making this method extremely tractable for high-dimensional systems. Our scalable sensor and actuator placement algorithm is demonstrated on the linearized Ginzburg-Landau system, resulting in the well-known optimal placements computed via gradient descent methods, at a fraction of the cost. |
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