Data-driven construction of a reduced-order model for supersonic boundary layer transition

2019 ◽  
Vol 874 ◽  
pp. 1096-1114 ◽  
Author(s):  
Ming Yu ◽  
Wei-Xi Huang ◽  
Chun-Xiao Xu
Keyword(s):  
Compressible Flows ◽  
Incompressible Flows ◽  
Temporal Evolution ◽  
Reduced Order Model ◽  
Boundary Layer Transition ◽  
Galerkin Projection ◽  
Data Driven ◽  
Dynamic Mode ◽  
Order Model ◽  
Reduced Order

In this study, a data-driven method for the construction of a reduced-order model (ROM) for complex flows is proposed. The method uses the proper orthogonal decomposition (POD) modes as the orthogonal basis and the dynamic mode decomposition method to obtain linear equations for the temporal evolution coefficients of the modes. This method eliminates the need for the governing equations of the flows involved, and therefore saves the effort of deriving the projected equations and proving their consistency, convergence and stability, as required by the conventional Galerkin projection method, which has been successfully applied to incompressible flows but is hard to extend to compressible flows. Using a sparsity-promoting algorithm, the dimensionality of the ROM is further reduced to a minimum. The ROMs of the natural and bypass transitions of supersonic boundary layers at $Ma=2.25$ are constructed by the proposed data-driven method. The temporal evolution of the POD modes shows good agreement with that obtained by direct numerical simulations in both cases.

scholarly journals A higher-order parametric nonlinear reduced-order model for imperfect structures using Neumann expansion

2021 ◽  
Author(s):  
J. Marconi ◽  
P. Tiso ◽  
D. E. Quadrelli ◽  
F. Braghin
Keyword(s):  
Reduced Order Model ◽  
Galerkin Projection ◽  
Order Model ◽  
Displacement Fields ◽  
Reduced Order ◽  
Total Displacement ◽  
Elastic Forces ◽  
Strain Formulation ◽  
The One ◽  
Definition Of

AbstractWe present an enhanced version of the parametric nonlinear reduced-order model for shape imperfections in structural dynamics we studied in a previous work. In this model, the total displacement is split between the one due to the presence of a shape defect and the one due to the motion of the structure. This allows to expand the two fields independently using different bases. The defected geometry is described by some user-defined displacement fields which can be embedded in the strain formulation. This way, a polynomial function of both the defect field and actual displacement field provides the nonlinear internal elastic forces. The latter can be thus expressed using tensors, and owning the reduction in size of the model given by a Galerkin projection, high simulation speedups can be achieved. We show that the adopted deformation framework, exploiting Neumann expansion in the definition of the strains, leads to better accuracy as compared to the previous work. Two numerical examples of a clamped beam and a MEMS gyroscope finally demonstrate the benefits of the method in terms of speed and increased accuracy.

A reduced order model to simulate compressible flows over an actuated riblet surface

2019 ◽  
Vol 348 ◽  
pp. 234-256
Author(s):  
G. Deolmi ◽  
S. Müller ◽  
M. Albers ◽  
P.S. Meysonnat ◽  
W. Schröder
Keyword(s):  
Compressible Flows ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Riblet Surface

scholarly journals Data-driven Reduced Order Model for prediction of wind turbine wakes

2015 ◽  
Vol 625 ◽  
pp. 012009 ◽  
Author(s):  
G V Iungo ◽  
C Santoni-Ortiz ◽  
M Abkar ◽  
F Porté-Agel ◽  
M A Rotea ◽  
...  
Keyword(s):  
Wind Turbine ◽  
Reduced Order Model ◽  
Data Driven ◽  
Order Model ◽  
Reduced Order

scholarly journals Evolve Then Filter Regularization for Stochastic Reduced Order Modeling

2018 ◽  
Author(s):  
Xuping Xie ◽  
Feng Bao ◽  
Clayton G. Webster
Keyword(s):  
Stochastic Systems ◽  
Spatial Filter ◽  
Reduced Order Modeling ◽  
Reduced Order Model ◽  
Galerkin Projection ◽  
Order Model ◽  
Reduced Order ◽  
Stochastic Burgers Equation ◽  
Numerical Stabilization ◽  
Convection Dominated

In this paper, we introduce the evolve-then-filter (EF) regularization method for reduced order modeling of convection-dominated stochastic systems. The standard Galerkin projection reduced order model (G-ROM) yield numerical oscillations in a convection-dominated regime. The evolve-then-filter reduced order model (EF-ROM) aims at the numerical stabilization of the standard G-ROM, which uses explicit ROM spatial filter to regularize various terms in the reduced order model (ROM). Our numerical results based on a stochastic Burgers equation with linear multiplicative noise. It shows that the EF-ROM is significantly better results than G-ROM.

Reduced Order Model for Unsteady Fluid Flows via Recurrent Neural Networks

2019 ◽  
Author(s):  
Sandeep B. Reddy ◽  
Allan Ross Magee ◽  
Rajeev K. Jaiman ◽  
J. Liu ◽  
W. Xu ◽  
...  
Keyword(s):  
Neural Networks ◽  
Reynolds Number ◽  
Flow Field ◽  
Unsteady Flow ◽  
Recurrent Neural Networks ◽  
Reduced Order Model ◽  
Data Driven ◽  
Order Model ◽  
Reduced Order ◽  
Low Dimensional

Abstract In this paper, we present a data-driven approach to construct a reduced-order model (ROM) for the unsteady flow field and fluid-structure interaction. This proposed approach relies on (i) a projection of the high-dimensional data from the Navier-Stokes equations to a low-dimensional subspace using the proper orthogonal decomposition (POD) and (ii) integration of the low-dimensional model with the recurrent neural networks. For the hybrid ROM formulation, we consider long short term memory networks with encoder-decoder architecture, which is a special variant of recurrent neural networks. The mathematical structure of recurrent neural networks embodies a non-linear state space form of the underlying dynamical behavior. This particular attribute of an RNN makes it suitable for non-linear unsteady flow problems. In the proposed hybrid RNN method, the spatial and temporal features of the unsteady flow system are captured separately. Time-invariant modes obtained by low-order projection embodies the spatial features of the flow field, while the temporal behavior of the corresponding modal coefficients is learned via recurrent neural networks. The effectiveness of the proposed method is first demonstrated on a canonical problem of flow past a cylinder at low Reynolds number. With regard to a practical marine/offshore engineering demonstration, we have applied and examined the reliability of the proposed data-driven framework for the predictions of vortex-induced vibrations of a flexible offshore riser at high Reynolds number.

scholarly journals Data-driven POD-Galerkin reduced order model for turbulent flows

2020 ◽  
Vol 416 ◽  
pp. 109513 ◽  
Author(s):  
Saddam Hijazi ◽  
Giovanni Stabile ◽  
Andrea Mola ◽  
Gianluigi Rozza
Keyword(s):  
Turbulent Flows ◽  
Reduced Order Model ◽  
Data Driven ◽  
Order Model ◽  
Reduced Order
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