In the Spring 2019 Semester, the Center of Mathematical Sciences and Applications will be hosting a seminar on Fluid Dynamics. The seminar will take place on Wednesdays from 3:00-4:00pm in CMSA G10.
Date | Speaker | Title/Abstract |
2/20/2019 | Xiaolin Wang, Harvard | Title: The effect of piezoelectric material on the stability of flexible flags
Abstract: Piezoelectric material has drawn enormous attention in recent decades due to its ability to convert mechanical deformation energy into electrical potential energy, and vice versa. It has been applied to both energy harvesting and passive vibration control applications. In this talk, we will discuss the effect of piezoelectric material on the stability of a flexible flag using a fully coupled fluid-solid-electric model. An inviscid vortex-sheet model and a linear electro-mechanical model are combined to describe the problem. We find that the critical flutter speed is increased due to the extra damping effect of piezoelectric material, and can also be altered by tuning the output inductance-resistance circuit. Optimal resistances and inductances are found that either maximize or minimize the flutter speed. The former application is useful for vibration control while the latter is important for energy harvesting. |
3/6/2019 | Zhong Yi Wan, MIT | Title: Machine learning the kinematics of spherical particles in fluid flows
Abstract: Numerous efforts have been devoted to the derivation of equations describing the kinematics of finite-size spherical particles in arbitrary fluid flows. These approaches rely on asymptotic arguments to obtain a description of the particle motion in terms of a slow manifold. We present a novel approach that results in kinematic models with unprecedented accuracy compared with traditional methods. We apply a recently developed machine learning framework that relies on (i) an imperfect model, obtained through analytical arguments, and (ii) a long short-term memory (LSTM) recurrent neural network. The latter learns the mismatch between the analytical model and the exact velocity of the finite-size particle as a function of the fluid velocity that the particle has encountered along its trajectory. We show that training the model for one flow is sufficient to generate accurate predictions for any other arbitrary flow field, capturing the spectrum of the particle velocity, as well as the extreme event statistics. The proposed scheme paves the way for machine learning kinematic models for bubbles and aerosols using high-fidelity DNS simulations and experiments. |
3/20/2019 | Paris Perdikaris, University of Pennsylvania | Title: Data-driven modeling of stochastic systems using physics-aware deep learning
Abstract: We present a probabilistic deep learning methodology that enables the construction of predictive data-driven surrogates for stochastic systems. Leveraging recent advances in variational inference, we put forth a scalable computational framework for discovering surrogate models from paired input-output observations of a system that may be stochastic in nature, originate from different information sources of variable fidelity, or be corrupted by complex noise processes. We also show how physical constraints can be employed as informative priors that introduce a regularization mechanism for effectively constructing robust deep learning models in cases where the cost of data acquisition is high and training data-sets are typically small. The effectiveness of the proposed methods is demonstrated through a series of canonical studies involving stochastic dynamical systems and nonlinear conservation laws. |
4/3/2019
Room G02 4pm |
Christopher Rycroft, Harvard | Title: The reference map technique for simulating complex materials and multi-body interactions
Abstract: Conventional computational methods often create a dilemma for fluid–structure interaction problems. Typically, solids are simulated using a Lagrangian approach with grid that moves with the material, whereas fluids are simulated using an Eulerian approach with a fixed spatial grid, requiring some type of interfacial coupling between the two different perspectives. Here, a fully Eulerian method for simulating structures immersed in a fluid will be presented. By introducing a reference map variable to model finite-deformation constitutive relations in the structures on the same grid as the fluid, the interfacial coupling problem is highly simplified. The method is particularly well suited for simulating soft, highly-deformable materials and many-body contact problems, and several examples will be presented. This is joint work with Ken Kamrin (MIT). |
4/10/2019
Science Center 530 |
Luc Deike, Princeton | Title: Wave breaking in ocean atmosphere interactions
Abstract: Breaking waves at the water surface is a striking example of turbulent mixing across a fluid interface. The impact of the jet generates turbulence, entrains air into the water and ejects droplets into the air. A fundamental understanding of the general multi-scale properties of the resulting air-water turbulent flow is necessary to develop more accurate gas transfer or spray generation parameterizations. I will discuss a multi-scale approach where air entrainment, bubble statistics and aerosol generation by bubble bursting is investigated by laboratory experiments and numerical simulations at small scale while ocean scale fluxes are obtained by up-scaling the results using statistical description of the wave and wave breaking field. This approach leads to semi-empirical formulations to be implemented in coupled ocean-wave models. |
4/17/2019
CMSA G02 |
Maziar Raissi, Nvidia | Title: Hidden Physics Models: Machine Learning of Non-Linear Partial Differential Equations
Abstract: A grand challenge with great opportunities is to develop a coherent framework that enables blending conservation laws, physical principles, and/or phenomenological behaviors expressed by differential equations with the vast data sets available in many fields of engineering, science, and technology. At the intersection of probabilistic machine learning, deep learning, and scientific computations, this work is pursuing the overall vision to establish promising new directions for harnessing the long-standing developments of classical methods in applied mathematics and mathematical physics to design learning machines with the ability to operate in complex domains without requiring large quantities of data. To materialize this vision, this work is exploring two complementary directions: (1) designing data-efficient learning machines capable of leveraging the underlying laws of physics, expressed by time dependent and non-linear differential equations, to extract patterns from high-dimensional data generated from experiments, and (2) designing novel numerical algorithms that can seamlessly blend equations and noisy multi-fidelity data, infer latent quantities of interest (e.g., the solution to a differential equation), and naturally quantify uncertainty in computations. The latter is aligned in spirit with the emerging field of probabilistic numerics. |
4/24/2019 | Heng Xiao (Virginia Tech) | Title: Turbulence Modeling in the Age of Data: From Data Assimilation to Machine Learning
Abstract: Many complex systems are characterized by physics at a wide range of scales, for which first-principle-based high-fidelity models resolving all the scales are prohibitively expensive to run. Consequently, practical simulations have primarily relied on low-fidelity models with approximate closure models, which introduce large model-form uncertainties and diminish their predictive capabilities. Turbulent flows are a classical example of such complex physical systems, where numerical solvers with turbulence closure models are widely used in industrial flow simulations. In light of the decades-long stagnation in traditional turbulence modeling, data-driven methods have been proposed as a promising alternative. We present a comprehensive framework for using data to reduce model uncertainties in turbulent flow simulations. For online, continuously streamed monitoring data, we use data assimilation and Bayesian inference to reduce model-form uncertainties; For offline data from a database of flows, we proposed a physics-informed machine learning approach to reduce model discrepancies. In both cases, we emphasized enforcing physical constraints in the data-driven modeling. More information: https://www.aoe.vt.edu/people/faculty/xiaoheng/personal-page/publications.html |
4/25/2019
12:00pm |
Neel Patel (University of Michigan) | Title: Local Existence and Blow-Up for SQG Patches
Abstract: We consider the evolution of sharp temperature fronts in the two-dimensional surface quasi-geostrophic (SQG) equation. This equation has been used as a model for atmospheric or oceanic flows and has structural similarity with the 3D Euler equation. The α-patch problem for 0 ≤ α ≤ 1 studies the evolution of patch solutions to a family of transport equations, where α = 0 and α = 1 correspond to the Euler vortex patches and the SQG sharp temperature fronts respectively. Previously, finite time singularities have been demonstrated on the half-plane setting for the family of functions 0 < α < 1/12 by first establishing local well-posedness of the system for that range and then constructing a blow-up solution. In this talk, we extend that result to 0 < α < 1/3 by exploring a new cancellation in the patch contour equation. Furthermore, this cancellation can be used to prove a singularity criterion of lower regularity than the numerical results for SQG patches and to prove lower regularity local existence results for the extended family of equations 0 < α < 2. |
5/1/2019
CMSA G02 |
David Sondak, IACS, Harvard | Title: Towards Machine Learning for Cataloguing Optimal Solutions in Turbulent Convection
Abstract: Fluids have had a profound impact on scientific and engineering pursuits. They impact life at its most basic levels (e.g. biological fluids) but are also found in astrophysical environments (e.g. solar physics). Moreover, understanding and working with fluids has significant implications for engineering systems. For example, fluids are good at transporting energy in the form of heat. In order to work efficiently with fluids, engineers and scientists must be able to predict forces that fluids exert on their surroundings. This is a major challenge, further confounded by the phenomenon of turbulence in which fluid flows are disordered and erratic. Understanding and predicting turbulent flows is a major open problem in classical physics with numerous practical applications. In this talk, optimal solutions that maximize heat transport in turbulent Rayleigh-Bénard convection are presented. The talk begins with an overview of fluid mechanics, turbulence, and Rayleigh-Bénard convection before introducing the idea of optimal solutions, their computation, and their relevance to turbulence. The second half of the talk will focus on methods for detecting the signature of these optimal solutions. Machine learning algorithms may provide new routes forward for detecting the optimal solutions in a turbulent flow. The talk will close with an application of autoencoders on a turbulent dataset in an effort to discern some of the building-blocks of turbulence. |
5/15/2019 | Tamer A. Zaki | Title: The Onset of Chaos in Shear Flows
Abstract: The manner in which infinitesimal disturbances can cause organized fluid motion to become chaotic is an intriguing phenomenon. In addition to being of great theoretical interest, laminar-to-turbulence transition is of significant importance due to its role in heat transfer, its influence on momentum mixing, and its effect on drag. In this work, we present complementary theoretical analyses, high-fidelity direct numerical simulations and data-enabled predictions of transition to turbulence in boundary layers. The proceedings of transition are not unique, and various pathways can ultimately lead to boundary-layer turbulence. In real-world applications, the presence of free-stream disturbances promotes early onset of turbulence, and transition is said to “bypass” other routes that have been traditionally examined using stability theory. Numerical simulations of this bypass transition process reveal that high-frequency disturbances from the free stream are expelled by the boundary-layer shear – a phenomenon known as shear sheltering. Using asymptotic analysis, we develop a physical understanding of the mechanics of shear sheltering, and explain how low-frequency free-stream perturbations can permeate the mean shear. These elongated disturbances force the boundary layer resonantly and lead to the amplification of streaks. While the majority of the laminar streaks are innocuous, a small proportion undergoes a localized instability and breaks down to turbulence. Reports in the literature present conflicting views on the origin of streak breakdown – a matter that we address by performing secondary instability analyses of realistic streaks as well as using artificial neural networks. The predicted streak instabilities are shown to cause breakdown to turbulence in complementary direct numerical |
5/22/2019 | Jörn Dunkel (MIT) |
Title: Symmetry breaking in active and quantum fluids
Abstract:Active biological fluids, such as bacterial and other microbial suspensions, exhibit striking spontaneous symmetry breaking phenomena, from the formation of vortex lattices to the emergence of large-scale unidirectional flows. Borrowing ideas from classical pattern formation theory, I will discuss generalized Navier-Stokes (GNS) equations as an analytically tractable minimal model of stress-driven active fluids. The GNS equations permit exact stress-free bulk solutions in planar and curved geometries, including Abrikosov-type lattices in 2D and Beltrami flows in 3D. A triad analysis shows that the combination of a generic linear instability and a standard advective nonlinearity can give rise to spontaneous chiral symmetry breaking that supports inverse energy transport in 3D. In the second part, we extend the underlying concepts to quantum fluids by deriving a higher-order generalization of the Gross-Pitaevskii equation to study supersolid crystals and quasi-crystals. |