Bulletin of the American Physical Society
74th Annual Meeting of the APS Division of Fluid Dynamics
Volume 66, Number 17
Sunday–Tuesday, November 21–23, 2021; Phoenix Convention Center, Phoenix, Arizona
Session Q31: Nonlinear Dynamics: Model Reduction & Turbulence V |
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Chair: Daniel Floryan, University of Houston Room: North 232 ABC |
Tuesday, November 23, 2021 8:00AM - 8:13AM |
Q31.00001: Gappy data reconstruction using SPOD Oliver T. T Schmidt, Akhil Nekkanti Spatio-temporal flow data, for example those obtained by time-resolved particle image velocimetry (PIV), often contain gaps or other types of undesired artifacts. To reconstruct flow data in the compromised regions, we propose a method based on spectral proper orthogonal decomposition (SPOD). The mathematical properties of SPOD make it well-suited for this task. In particular, the proposed approach leverages the temporal correlation with preceding and succeeding snapshots in time, as well as the correlation with the surrounding data in space. The algorithm involves the computation of the SPOD from the data that is not affected by any given gap and an inversion of the SPOD to reconstruct the data in the affected regions. We test the method for two data sets: the canonical example of numerical data of laminar flow past a cylinder and the more challenging (and relevant) case of PIV data of turbulent cavity flow. Three levels of gappiness, 1%, 5%, and 20% are considered. |
Tuesday, November 23, 2021 8:13AM - 8:26AM |
Q31.00002: Kernel Mode Decomposition for Time-Frequency Localization of Transient Flow Tso-Kang Wang, Kourosh Shoele Kernel mode decomposition (KMD) is a powerful method to identify modes with varying amplitude and frequency. This work aims to extend this technique to study different fluid problems with transient responses to reveal and evolve the relevant spatial structures. The results are compared to other modal decomposition methods and show good agreement in the spatial modes, while the proposed KMD method is capable of isolating the important scales inherently. The KMD works with any signal by comparing the input to very fine modes then combine the fine modes based on the extent of alignment to recover the dominant components. The many benefits of KMD include that it does not involve any learning process, it is modular and interpretable with each step being mathematically derived, and it is easy to modify for different scenarios such as using different base waveforms as the fine modes. |
Tuesday, November 23, 2021 8:26AM - 8:39AM |
Q31.00003: On-the-fly Compression of Simulating Data Using Time-Dependent Basis Shaghayegh Zamani Ashtiani, Mujeeb R Malik, Hessam Babaee Exascale computation enables numerical solution of large-scale and high-fidelity problems. Memory and I/O restriction impede data analysis and visualization of many high-fidelity scientific computing applications — particularly transient problems. Therefore, developing an in situ compression method to compress the streaming data in real-time is vital. We present an on-the-fly dimension reduction technique that does not require calculation of large-scale eigenvalues problems. Instead, a scalable algorithm for the on-the-fly decomposition of the streaming data into a set of time-dependent bases and a core tensor is presented. The presented method is adaptive, and the reduction error is controlled by mode addition or removal. Several demonstration examples, including on-the-fly compression of the direct numerical simulation of turbulent flow, are presented. |
Tuesday, November 23, 2021 8:39AM - 8:52AM Not Participating |
Q31.00004: A hybrid modeling approach for coupling reduced order and full order models of the Boussinesq system Mehrdad Zomorodiyan, Shady E Ahmed, Omer San Multiphysics solvers addressing problems with different computational costs for the coupled physics are limited by the most computationally expensive routines (e.g., solving the Poisson equation in incompressible flow solvers). In this work, we replace the costly part with an interactive non-intrusive machine learning (ML) model so that we could benefit from the robustness of the ML and accuracy and generalisability of the full order model (FOM) for the focus of the solution. Specifically, we model the evolution of the proper orthogonal decomposition modal amplitudes of the vorticity transport and continuity equations using a long short-term memory (LSTM) neural network, coupled with the FOM solution of the energy equation. This ROM-FOM coupling framework solves the Boussinesq equations for the lock-exchange problem to demonstrate the benefits of this multi-fidelity setup. |
Tuesday, November 23, 2021 8:52AM - 9:05AM |
Q31.00005: Data-driven sensor placement for fluid flows Palash Sashittal, Daniel J Bodony Sensor placement for complex fluid flows is an important and challenging problem. In this talk, we present a completely data-driven and computationally efficient method for sensor placement in fluid flows. Our method leverages recent advances in data-driven reduced-order modeling and minimizes an empirical measure of the error covariance matrix. We also propose an augmented objective function for feedback control applications. We demonstrate the performance of our method for reconstruction and prediction of the complex linearized Ginzburg–Landau equation in the globally unstable regime. We also construct a low-dimensional observer-based feedback controller for the flow over an inclined flat plate that is able to suppress the wake vortex shedding in the presence of system and measurement noise. |
Tuesday, November 23, 2021 9:05AM - 9:18AM |
Q31.00006: A sparse optimal closure for a reduced-order model of wall-bounded turbulence. Chi Hin Chan, Zhao Chua Khoo, Yongyun Hwang In the present study, a set of physics-informed and data-driven approaches are examined towards the development of an accurate reduced-order model for a fully-developed turbulent plane Couette flow. Based on the utilisation of the proper orthogonal decomposition (POD) modes, a focus is given on the development of a reduced-order model where the number of the POD modes is not large enough to cover the full dynamics of the given turbulent state, the situation directly relevant to the reduced-order modelling for turbulent flows. Starting from the conventional Galerkin projection approach ignoring the truncation error, three approaches enhanced by both physics and data are examined: 1) sparse regression of the POD-Galerkin dynamics; 2) Galerkin projection with an empirical eddy viscosity model; 3) Galerkin projection with an optimal eddy viscosity obtained from a newly-proposed sparse regression. The sparse regression of the POD-Galerkin dynamics is found to result in an unsuccessful reduced-order model with the solution blow-up due to the too-small number of POD modes to resolve the given chaotic dynamics. While the unsatisfactory performance of the Galerkin-projection-based model with an empirical eddy viscosity is observed, the newly proposed approach, which combines the concept of optimal eddy-viscosity closure with a sparse regression, accurately approximates the chaotic dynamics. This is demonstrated with the mean and time scale of the POD mode amplitudes as well as with first- and second-order turbulence statistics. |
Tuesday, November 23, 2021 9:18AM - 9:31AM |
Q31.00007: Attention-based Convolutional Recurrent Autoencoder for Learning Wave Propagation Indu Kant Deo, Rajeev K Jaiman While forward analysis using hyperbolic partial differential equations is quite successful in modeling wave propagation phenomena, these phenomena pose challenges in dimensionality reduction and inverse modeling. To forecast time-series of wave propagation, we present a novel attention-based convolutional recurrent autoencoder (AB-CRAN) as a reduced-order model based on a domain-specific deep learning algorithm. The proposed AB-CRAN employs a denoising convolutional autoencoder to project the high-dimensional data to a low-dimensional nonlinear manifold and an attention-based sequence-to-sequence long short-term memory network to evolve these low-dimensional representations in time. A hybrid loss function is constructed by combining the autoencoder and propagator contributions into a single loss. In order to learn the optimal weights, a new supervised-unsupervised training strategy is devised. We demonstrate the effectiveness of our model on three benchmark problems: (i) one-dimensional linear convection with periodic boundary conditions, (ii) one-dimensional viscous Burgers' equation with Dirichlet boundary conditions, and (iii) 2D wave propagation in shallow water. On all data sets, AB-CRAN accurately captures the wave amplitude and learns the wave propagation in time. |
Tuesday, November 23, 2021 9:31AM - 9:44AM |
Q31.00008: Integration of slow--fast quasilinear models of turbulent shear flows Alessia Ferraro, Gregory Chini, Tobias M Schneider The quasilinear (QL) reduction, which retains fluctuation-fluctuation nonlinearities only where they feed back onto mean fields, is often employed as a model reduction strategy. This approximation can be justified in the limit of temporal scale separation between the mean and fluctuation dynamics as arises, e.g., in the asymptotic description of strongly stratified shear turbulence and of exact coherent states (ECS) in wall-bounded shear flows. Here, we utilize carefully constructed model problems to derive two important extensions to our recently introduced formalism for integrating slow--fast QL systems, which exploits the tendency of these systems to self-organize about a marginal stability manifold and slaves the amplitude of the (marginal) fluctuations to the slowly-evolving mean field. The first extension accommodates large-amplitude bursting events, in which temporal scale separation is transiently lost until marginal stability is re-established. The second extension yields a slow equation for the wavenumber of the marginal mode. Together, these extensions enable scale-selective adaptivity in both space and time. Our formalism is consistent with the idea that shear flow turbulence tracks low-d ECS during slow evolutionary phases punctuated by intermittent bursting events. |
Tuesday, November 23, 2021 9:44AM - 9:57AM |
Q31.00009: Determination of distinct dynamical process in the flow using machine learning Serena Costanzo, Miguel Fosas de Pando, Taraneh Sayadi, Peter J Schmid, Pascal Frey With advances in computing power, larger flow simulations are being performed, producing ever-increasing amounts of data and calling for data-driven techniques, such as system identification and machine learning, to analyse the flow fields. These techniques can in turn be extended to guide model reduction and model design efforts for complex configurations. Taking projection-based model reduction techniques, for example, system identification can be utilised to infer nonlinear coupling between the predetermined modes. The resulting models are particularly suited for control applications, since, by design, the captured dynamics are part of the observed input-output behaviour of the system. However, due to missing information on the nonlinear dynamics of the flow, this reduction procedure faces limitations when applied to complex flow configurations. Alternatively, the identification process can be redirected to discover the dominant dynamics in the flow using machine learning techniques directly on the data rather than extract a basis in which to express it. This work introduces one such algorithm where the active terms in the equation governing the flow (the Navier-Stokes equation) are identified using linear regression techniques, and the recovered coefficients characterize the different dynamics present in the flow. Clustering algorithms are then applied on these coefficients to define different regions of the computational domain with an associated, and distinct dynamics. This method has been applied and validated on various flow configurations using an incompressible Navier-Stokes solver. |
Tuesday, November 23, 2021 9:57AM - 10:10AM |
Q31.00010: Rayleigh-Bénard convection in Spherical Shells using Discrete Exterior Calculus and Finite Difference Hybrid Method Bhargav Mantravadi, Pankaj Jagad, Ravi Samtaney Solar convection is a highly complex phenomenon characterized by turbulent buoyant flows, differential rotation, and self-generation and sustenance of magnetic fields due to convective plasma motions. The spherical geometry and extreme lim- its of the non-dimensional numbers pose a major challenge in simulating this phe- nomenon. Given the unique features of discrete exterior calculus (DEC), for in- stance, exact discretization, ability to simulate flows on curved surfaces, coordinate independence, conservation of secondary quantities, we have developed a hybrid discrete exterior calculus and finite difference (DEC-FD) method to simulate fully three-dimensional Boussinesq convection in spherical shells. We present several test cases of Rayleigh-Bénard convection in the linear and weakly non-linear regime. In the linear regime, we quantify the kinetic energy decay, and compare with the analytical solution. In the weakly non-linear regime, for moderately thin shells, we simulate the single spiral roll state, and the steady state kinetic energies for different Prandtl numbers are in very close agreement with Li et al. (Phys. Rev. E, 2005). Furthermore, we will examine RBC for extreme regimes(Rayleigh number ≥ 109). |
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