scholarly journals Long-time Reynolds averaging of reduced order models for fluid flows: Preliminary results

2020 ◽  
Vol 2 (1) ◽  
pp. 1-25 ◽  
Author(s):  
Luigi C. Berselli ◽  
◽  
Traian Iliescu ◽  
Birgul Koc ◽  
Roger Lewandowski ◽  
...  
Keyword(s):  
Fluid Flows ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Preliminary Results ◽  
Long Time ◽  
Reynolds Averaging

scholarly journals Construction of reduced-order models for fluid flows using deep feedforward neural networks

2019 ◽  
Vol 872 ◽  
pp. 963-994 ◽  
Author(s):  
Hugo F. S. Lui ◽  
William R. Wolf
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Fluid Flows ◽  
Leading Edge ◽  
Feedforward Neural Networks ◽  
Orthogonal Decomposition ◽  
Reduced Order Models ◽  
Order Model ◽  
Sparse Regression ◽  
Reduced Order ◽  
Proper Orthogonal

We present a numerical methodology for construction of reduced-order models (ROMs) of fluid flows through the combination of flow modal decomposition and regression analysis. Spectral proper orthogonal decomposition is applied to reduce the dimensionality of the model and, at the same time, filter the proper orthogonal decomposition temporal modes. The regression step is performed by a deep feedforward neural network (DNN), and the current framework is implemented in a context similar to the sparse identification of nonlinear dynamics algorithm. A discussion on the optimization of the DNN hyperparameters is provided for obtaining the best ROMs and an assessment of these models is presented for a canonical nonlinear oscillator and the compressible flow past a cylinder. Then the method is tested on the reconstruction of a turbulent flow computed by a large eddy simulation of a plunging airfoil under dynamic stall. The reduced-order model is able to capture the dynamics of the leading edge stall vortex and the subsequent trailing edge vortex. For the cases analysed, the numerical framework allows the prediction of the flow field beyond the training window using larger time increments than those employed by the full-order model. We also demonstrate the robustness of the current ROMs constructed via DNNs through a comparison with sparse regression. The DNN approach is able to learn transient features of the flow and presents more accurate and stable long-term predictions compared to sparse regression.

scholarly journals Real-Time Simulation of Parameter-Dependent Fluid Flows through Deep Learning-Based Reduced Order Models

Fluids ◽  
2021 ◽  
Vol 6 (7) ◽  
pp. 259
Author(s):  
Stefania Fresca ◽  
Andrea Manzoni
Keyword(s):  
Deep Learning ◽  
Real Time ◽  
Elastic Beam ◽  
Fluid Flows ◽  
Reduced Order Models ◽  
Fluid Structure ◽  
Reduced Order ◽  
Reduction Strategies ◽  
Pressure Formulation ◽  
Parameter Dependent

Simulating fluid flows in different virtual scenarios is of key importance in engineering applications. However, high-fidelity, full-order models relying, e.g., on the finite element method, are unaffordable whenever fluid flows must be simulated in almost real-time. Reduced order models (ROMs) relying, e.g., on proper orthogonal decomposition (POD) provide reliable approximations to parameter-dependent fluid dynamics problems in rapid times. However, they might require expensive hyper-reduction strategies for handling parameterized nonlinear terms, and enriched reduced spaces (or Petrov–Galerkin projections) if a mixed velocity–pressure formulation is considered, possibly hampering the evaluation of reliable solutions in real-time. Dealing with fluid–structure interactions entails even greater difficulties. The proposed deep learning (DL)-based ROMs overcome all these limitations by learning, in a nonintrusive way, both the nonlinear trial manifold and the reduced dynamics. To do so, they rely on deep neural networks, after performing a former dimensionality reduction through POD, enhancing their training times substantially. The resulting POD-DL-ROMs are shown to provide accurate results in almost real-time for the flow around a cylinder benchmark, the fluid–structure interaction between an elastic beam attached to a fixed, rigid block and a laminar incompressible flow, and the blood flow in a cerebral aneurysm.

scholarly journals Sum-of-squares approach to feedback control of laminar wake flows

2016 ◽  
Vol 809 ◽  
pp. 628-663 ◽  
Author(s):  
Davide Lasagna ◽  
Deqing Huang ◽  
Owen R. Tutty ◽  
Sergei Chernyshenko
Keyword(s):  
Feedback Control ◽  
Kinetic Energy ◽  
Polynomial Function ◽  
Control Design ◽  
Fluid Flows ◽  
Sum Of Squares ◽  
Galerkin Projection ◽  
Reduced Order ◽  
Long Time ◽  
Time Averages

In this paper a novel nonlinear feedback control design methodology for incompressible fluid flows aiming at the optimisation of long-time averages of flow quantities is presented. It applies to reduced-order finite-dimensional models of fluid flows, expressed as a set of first-order nonlinear ordinary differential equations with the right-hand side being a polynomial function in the state variables and in the controls. The key idea, first discussed in Chernyshenko et al. (Phil. Trans. R. Soc. Lond. A, vol. 372, 2014, 20130350), is that the difficulties of treating and optimising long-time averages of a cost are relaxed by using the upper/lower bounds of such averages as the objective function. In this setting, control design reduces to finding a feedback controller that optimises the bound, subject to a polynomial inequality constraint involving the cost function, the nonlinear system, the controller itself and a tunable polynomial function. A numerically tractable and efficient approach to the solution of such optimisation problems, based on sum-of-squares techniques and semidefinite programming, is proposed. To showcase the methodology, the mitigation of the fluctuation kinetic energy in the unsteady wake behind a circular cylinder in the laminar regime at $Re=100$, via controlled angular motions of the surface, is numerically investigated. A compact reduced-order model that resolves the long-term behaviour of the fluid flow and the effects of actuation, is first derived using proper orthogonal decomposition and Galerkin projection. In a full-information setting, feedback controllers are then designed to reduce the long-time average of the resolved kinetic energy associated with the limit cycle. These controllers are then implemented in direct numerical simulations of the actuated flow. Control performance, total energy efficiency and the physical control mechanisms identified are analysed in detail. Key elements of the methodology, implications and future work are finally discussed.

Energy balance and mass conservation in reduced order models of fluid flows

2017 ◽  
Vol 346 ◽  
pp. 262-277 ◽  
Author(s):  
Muhammad Mohebujjaman ◽  
Leo G. Rebholz ◽  
Xuping Xie ◽  
Traian Iliescu
Keyword(s):  
Energy Balance ◽  
Fluid Flows ◽  
Mass Conservation ◽  
Reduced Order Models ◽  
Reduced Order
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