Article
Engineering, Multidisciplinary
Victor Zucatti, William Wolf
Summary: A data-driven closure modeling approach based on proper orthogonal decomposition (POD) temporal modes is utilized to obtain stable and accurate reduced order models (ROMs) for unsteady compressible flows. Model reduction is achieved through Galerkin and Petrov-Galerkin projection of the non-conservative compressible Navier-Stokes equations. The study involves analysis of a canonical compressible cylinder flow and turbulent flow over a plunging airfoil undergoing dynamic stall, requiring regularization and iterative Tikhonov methodology.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Mathematics, Applied
Xi Li, Yan Luo, Minfu Feng
Summary: In this paper, an efficient proper orthogonal decomposition based reduced-order model (POD-ROM) for nonstationary Stokes equations is proposed. The new scheme combines the classical projection method with POD technique, resulting in low computational costs and improved efficiency.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Mechanics
Romit Maulik, Bethany Lusch, Prasanna Balaprakash
Summary: This study demonstrates that using a combination of convolutional autoencoders (CAEs) and recurrent neural networks effectively overcomes the limitations of the POD-Galerkin technique in advection-dominated nonlinear PDEs. Truncated systems with only a few latent space dimensions can accurately reproduce complex fluid dynamics phenomena, and parameter information can be easily embedded to detect trends in system evolution.
Article
Computer Science, Interdisciplinary Applications
Victor Zucatti, William Wolf, Michel Bergmann
Summary: Calibration analysis of reduced-order models (ROMs) was conducted in this work, testing Galerkin and least-squares Petrov-Galerkin (LSPG) methods on compressible flows with disparate temporal scales. A novel calibration strategy for LSPG method was proposed with analysis on two test cases. Results showed stable and accurate ROMs for both cases, and the impact of hyper reduction on LSPG models was evaluated. Different time-marching schemes were assessed, revealing Galerkin models to be more accurate than LSPG models in solving non-conservative form of the Navier-Stokes equations.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Engineering, Mechanical
Giorgio Gobat, Andrea Opreni, Stefania Fresca, Andrea Manzoni, Attilio Frangi
Summary: In this study, the Proper Orthogonal Decomposition (POD) method is applied to efficiently simulate the nonlinear behavior of Micro-Electro-Mechanical-Systems (MEMS) in various scenarios involving geometric and electrostatic nonlinearities. The POD method reduces the polynomial terms up to cubic order associated with large displacements through exact projection onto a low-dimensional subspace spanned by the Proper Orthogonal Modes (POMs). Electrostatic nonlinearities are modeled using precomputed manifolds based on the amplitudes of the electrically active POMs. The reliability of the assumed linear trial space is extensively tested in challenging applications such as resonators, micromirrors, and arches with internal resonances. Comparisons are made between the periodic orbits computed with POD and the invariant manifold approximated with Direct Normal Form approaches, highlighting the reliability and remarkable predictive capabilities of the technique, particularly in terms of estimating the frequency response function of selected output quantities of interest.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2022)
Article
Computer Science, Interdisciplinary Applications
Jorge Yanez, Andreas G. Class
Summary: A surrogate model of the Standard k-e turbulence model is created using Proper Orthogonal Decomposition and Galerkin projection, with the non-linearities of the turbulence model equations treated using the Discrete Empirical Interpolation method. A heuristic procedure has been developed to allow for practical usage of this methodology. The capabilities of the construct to reproduce the CFD calculation in nominal conditions are subsequently assessed.
COMPUTERS & FLUIDS
(2022)
Article
Engineering, Multidisciplinary
My Ha Dao, Hoang Huy Nguyen, Chin Chun Ooi, Quang Tuyen Le
Summary: This study presents a complete algorithm for constructing and solving a projection-based reduced order model coupled with an artificial neural network model, with the reduced model based on Galerkin projection and Proper Orthogonal Decomposition method, implemented using numerical discretization schemes in the OpenFOAM platform, and the neural network model trained with NARX architecture. The reduced order models accurately predict the behavior of incompressible flows at low Reynolds numbers, showing excellent agreement with full CFD simulations while requiring significantly fewer computational resources.
APPLIED MATHEMATICAL MODELLING
(2021)
Article
Mathematics, Applied
Kun Li, Ting-Zhu Huang, Liang Li, Stephane Lanteri
Summary: In this article, a reduced-order model (ROM) based on the proper orthogonal decomposition (POD) technique is proposed for modeling the interaction between light and nanometer-scale metallic structures described by the system of 3-D time-domain Maxwell's equations coupled to a Drude dispersion model. The ROM is constructed using the singular value decomposition (SVD) method and a Galerkin projection with a second order leap-frog (LF2) time discretization. The stability condition of the ROM is analyzed, showing that it preserves the stability characteristics of the original high dimensional model. Numerical experiments are presented to validate the accuracy and efficiency of the POD-based ROM for 3-D nanophotonic problems.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2023)
Article
Thermodynamics
Jiacheng Ma, Donghun Kim, James E. Braun
Summary: This paper presents a computationally efficient and accurate dynamic modeling approach for vapor compression systems using model order reduction techniques. By reformulating the heat exchanger model and applying POD, reduced order models for evaporator and condenser are constructed with system stability and numerical efficiency in mind. Transient simulations conducted under various operating conditions show that the reduced order model can execute faster with negligible prediction errors compared to the high-fidelity finite volume model.
INTERNATIONAL JOURNAL OF REFRIGERATION
(2021)
Article
Engineering, Multidisciplinary
Stefania Fresca, Andrea Manzoni
Summary: DL-ROMs are proposed to overcome limitations of conventional ROMs, but require expensive training. The proposed method combines POD and multi-fidelity pretraining to avoid the costly training stage of DL-ROMs.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Engineering, Multidisciplinary
Peter Benner, Jan Heiland
Summary: In this work, a multidimensional Galerkin proper orthogonal decomposition method is proposed to reduce the complexity of quantifying multivariate uncertainties in partial differential equations. The analytical framework and results are provided to define and quantify the low-dimensional approximation. An application for uncertainty modeling using polynomial chaos expansions is illustrated, showing the efficiency of the proposed method.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2023)
Article
Multidisciplinary Sciences
Kamil David Sommer, Lucas Reineking, Yogesh Parry Ravichandran, Romuald Skoda, Martin Monnigmann
Summary: This paper presents a method using a projection-based reduced order model (ROM) and extended Kalman filter to estimate the velocity and pressure fields of fluid flows inside a centrifugal pump in realtime. The measurement locations are optimized using a greedy algorithm and the robustness of the estimation is ensured with a time-variant observability matrix. The results of the ROMs and extended Kalman filter based on a 2D centrifugal pump simulation are also presented.
Article
Mechanics
B. Karasozen, S. Yildiz, M. Uzunca
Summary: In this paper, reduced-order models (ROMs) are developed for the rotating thermal shallow water equation (RTSWE) in the non-canonical Hamiltonian form with state-dependent Poisson matrix. The ROMs are constructed using proper orthogonal decomposition with Galerkin projection and integrated in time with the average vector field (AVF) method. The computational cost is reduced by approximating the nonlinear terms with the discrete empirical interpolation method. The accuracy and computational efficiency of the ROMs are demonstrated for a numerical test problem.
Article
Engineering, Civil
Bonchan Koo, Hyunsoo Kim, Taehyun Jo, Sangwoo Kim, Joon Yong Yoon
Summary: In this study, the POD-Galerkin projection method was used for model order reduction in the quasi-two-dimensional water-hammer problem. By reducing the number of degrees of freedom, the computational burden was alleviated, and the temporal behavior of the POD basis vectors was analyzed. The proposed method was validated using experimental data, and the computational cost and complexity were compared to demonstrate its accuracy and efficiency.
JOURNAL OF HYDRAULIC RESEARCH
(2021)
Article
Computer Science, Interdisciplinary Applications
Elizabeth H. Krath, Forrest L. Carpenter, Paul G. A. Cizmas, David A. Johnston
Summary: This study introduces a novel, more efficient reduced-order model for compressible flows based on proper orthogonal decomposition (POD). By using specific volume instead of density, the coefficients of the system of ODEs in the reduced-order model were pre-computed. Various methods were used to enhance ODE solver stability. Validation was done for two cases, showing a speedup exceeding four orders of magnitude compared to the full-order model.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Engineering, Mechanical
Karim Sherif, Karin Nachbagauer, Wolfgang Steiner
NONLINEAR DYNAMICS
(2015)
Article
Mechanics
Stefan Oberpeilsteiner, Thomas Lauss, Karin Nachbagauer, Wolfgang Steiner
MULTIBODY SYSTEM DYNAMICS
(2017)
Article
Mechanics
Thomas Lauss, Stefan Oberpeilsteiner, Wolfgang Steiner, Karin Nachbagauer
MULTIBODY SYSTEM DYNAMICS
(2018)
Article
Mechanics
Stefan Oberpeilsteiner, Thomas Lauss, Wolfgang Steiner, Karin Nachbagauer
MULTIBODY SYSTEM DYNAMICS
(2018)
Article
Mechanics
Wolfgang Steiner
Article
Automation & Control Systems
Wolfgang Steiner, Stefan Reichl
JOURNAL OF DYNAMIC SYSTEMS MEASUREMENT AND CONTROL-TRANSACTIONS OF THE ASME
(2012)
Article
Mechanics
Karim Sherif, Karin Nachbagauer, Wolfgang Steiner, Thomas Lauss
MULTIBODY SYSTEM DYNAMICS
(2019)
Article
Engineering, Mechanical
Thomas Lauss, Stefan Oberpeilsteiner, Wolfgang Steiner, Karin Nachbagauer
JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS
(2017)
Proceedings Paper
Engineering, Mechanical
Daniel Stadlmayr, Wolfgang Witteveen
NONLINEAR DYNAMICS, VOL 1
(2017)
Article
Engineering, Mechanical
Daniel Stadlmayr, Wolfgang Witteveen, Wolfgang Steiner
JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS
(2016)
Article
Engineering, Mechanical
Karin Nachbagauer, Stefan Oberpeilsteiner, Karim Sherif, Wolfgang Steiner
JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS
(2015)
Proceedings Paper
Engineering, Mechanical
Karim Sherif, Karin Nachbagauer, Stefan Oberpeilsteiner, Wolfgang Steiner
TOPICS IN MODAL ANALYSIS, VOL 10
(2015)