Boundary-Condition-Independent Reduced-Order Modeling of Heat Transfer in Complex Objects by POD-Galerkin Methodology: 1D Case Study

2010 ◽  
Vol 132 (6) ◽  
Author(s):  
Arun P. Raghupathy ◽  
Urmila Ghia ◽  
Karman Ghia ◽  
William Maltz
Keyword(s):  
Boundary Condition ◽  
Reduced Order Modeling ◽  
Technical Note ◽  
Reduced Order Models ◽  
Electronic Components ◽  
Complex Objects ◽  
Reduced Order ◽  
Volume Method ◽  
Proper Orthogonal

This technical note presents an introduction to boundary-condition-independent reduced-order modeling of complex electronic components using the proper orthogonal decomposition (POD)-Galerkin approach. The current work focuses on how the POD methodology can be used along with the finite volume method to generate reduced-order models that are independent of their boundary conditions. The proposed methodology is demonstrated for the transient 1D heat equation, and preliminary results are presented.

Reduced-Order Modeling of Unsteady Flows About Complex Configurations Using the Boundary Element Method

2002 ◽  
Vol 124 (4) ◽  
pp. 988-993 ◽  
Author(s):  
V. Esfahanian ◽  
M. Behbahani-nejad
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Three Dimensional ◽  
Unsteady Flows ◽  
Reduced Order Modeling ◽  
Element Formulation ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Naca 0012 ◽  
Element Method

An approach to developing a general technique for constructing reduced-order models of unsteady flows about three-dimensional complex geometries is presented. The boundary element method along with the potential flow is used to analyze unsteady flows over two-dimensional airfoils, three-dimensional wings, and wing-body configurations. Eigenanalysis of unsteady flows over a NACA 0012 airfoil, a three-dimensional wing with the NACA 0012 section and a wing-body configuration is performed in time domain based on the unsteady boundary element formulation. Reduced-order models are constructed with and without the static correction. The numerical results demonstrate the accuracy and efficiency of the present method in reduced-order modeling of unsteady flows over complex configurations.

scholarly journals Reduced Order Models for Nonlinear Dynamic Analysis With Application to a Fan Blade

2019 ◽  
Author(s):  
Mikel Balmaseda ◽  
G. Jacquet-Richardet ◽  
A. Placzek ◽  
D.-M. Tran
Keyword(s):  
Normal Modes ◽  
Nonlinear Dynamic Analysis ◽  
Evaluation Procedure ◽  
Reduced Order Models ◽  
Reduced Basis ◽  
Reduced Order ◽  
Stiffness Evaluation ◽  
Fan Blade ◽  
Proper Orthogonal ◽  
Good Agreement

Abstract In the present work reduced order models (ROM) that are independent from the full order finite element models (FOM) considering geometrical non linearities are developed and applied to the dynamic study of a fan. The structure is considered to present nonlinear vibrations around the pre-stressed equilibrium induced by rotation enhancing the classical linearised approach. The reduced nonlinear forces are represented by a polynomial expansion obtained by the Stiffness Evaluation Procedure (STEP) and then corrected by means of a Proper Orthogonal Decomposition (POD) that filters the full order nonlinear forces (StepC ROM). The Linear Normal Modes (LNM) and Craig-Bampton (C-B) type reduced basis are considered here. The latter are parametrised with respect to the rotating velocity. The periodic solutions obtained with the StepC ROM are in good agreement with the solutions of the FOM and are more accurate than the linearised ROM solutions and the STEP ROM. The proposed StepC ROM provides the best compromise between accuracy and time consumption of the ROM.

Comparison of two model reduction approaches of an industrial drying process

2021 ◽  
Vol 69 (8) ◽  
pp. 667-682
Author(s):  
Marc Oliver Berner ◽  
Martin Mönnigmann
Keyword(s):  
Dynamic Models ◽  
Orthogonal Decomposition ◽  
Wood Chips ◽  
Residual Water ◽  
Balanced Truncation ◽  
Reduced Order Models ◽  
Drying Process ◽  
Reduced Order ◽  
Proper Orthogonal ◽  
Many Particles

Abstract Dynamic models have proven to be helpful for determining the residual water content in combustible biomass. However, these models often require partial differential equations, which render simulations impracticable when several thousand particles need to be considered, such as in the drying of wood chips. Reduced-order models help to overcome this problem. We compare proper orthogonal decomposition (POD) based to balanced truncation based reduced-order models. Both reduced models are lean enough for an application to systems with many particles, but the model based on balanced truncation shows more accurate results.

scholarly journals Constrained reduced-order models based on proper orthogonal decomposition

2017 ◽  
Vol 321 ◽  
pp. 18-34 ◽  
Author(s):  
Sohail R. Reddy ◽  
Brian A. Freno ◽  
Paul G.A. Cizmas ◽  
Seckin Gokaltun ◽  
Dwayne McDaniel ◽  
...  
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Orthogonal Decomposition ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Proper Orthogonal

Hamilton’s Principle for Fluid-Structure Interaction and Applications to Reduced-Order Modeling

2005 ◽  
Author(s):  
Rene D. Gabbai ◽  
Haym Benaroya
Keyword(s):  
General Framework ◽  
Model Problem ◽  
Viscous Flows ◽  
Reduced Order Modeling ◽  
Reduced Order Models ◽  
Hamilton’S Principle ◽  
Governing Equations ◽  
Hamilton's Principle ◽  
Reduced Order ◽  
Structure Interaction

A general framework based on the extended Hamilton’s principle for external viscous flows is presented. The indicated method is shown to yield the correct governing equations and boundary conditions when applied to the problem (herein called the “model problem”) of vortex-induced oscillations of an elastically-mounted rigid circular cylinder with a transverse degree-of-freedom. The vortex shedding is assumed to be sufficiently correlated along the span of the cylinder that the flow can be taken as nominally two-dimensional. The incoming flow is assumed to be incompressible, steady, and uniform. The continuity equation results directly from the global mass balance law, thus avoiding its introduction via a Lagrange multiplier. The true strength of this framework lies in the fact that it represents a physically sound basis from which reduced-order models can be obtained. Some preliminary work on this reduced-order modeling applied to the model problem is described.

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.

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