Orthogonal Decomposition Reduced-order Model Research Articles

Numerical Analysis of a Projection-Based Stabilized POD-ROM for Incompressible Flows

In this paper, we propose a new stabilized projection-based proper orthogonal decomposition reduced order model (POD-ROM) for the numerical simulation of incompressible flows. The new method draws ...

POD-ROM for the Darcy–Brinkman equations with double-diffusive convection

Abstract This paper extends proper orthogonal decomposition reduced order modeling to flows governed by double diffusive convection, which models flow driven by two potentials with different rates of diffusion. We propose a reduced model based on proper orthogonal decomposition, present a stability and convergence analyses for it, and give results for numerical tests on a benchmark problem which show it is an effective approach to model reduction in this setting.

Semi-automated proper orthogonal decomposition reduced order model non-linear analysis for future BWR stability

Thermal–hydraulic coupling between power, flow rate and density, intensified by neutronics feedback are the main drivers determining the stability behavior of a boiling water reactor (BWR). High-power low-flow conditions in connection with unfavorable power distributions can lead the BWR system into unstable regions where power oscillations can be triggered. This important threat to operational safety requires careful analysis for proper understanding. Current design rules assure admissible operation conditions by exclusion regions determined by numerical calculations and analytical methods based on non-linear states for specific transients.Analyzing an exhaustive parameter space of the non-linear BWR system becomes feasible with methodologies based on reduced order models (ROMs), saving computational cost and improving the physical understanding. A new self-contained methodology is developed, based on the general general proper orthogonal decomposition (POD) reduction technique. It is mostly automated, applicable for generic partial differential equation (PDE) systems, and reduces them in a grid-free manner to a small ordinary differential equation (ODE) system able to capture even non-linear dynamics. This allows a much more extensive analysis of the represented physical system. Symbolic mathematical manipulations are performed automatically by Mathematica routines. A novel and general calibration roadmap is proposed which simplifies choices on specific POD variants when applying the ROMing to different fields of physics. Persecuting validation and verification, a wide and systematic spectrum of representative test examples has been treated.The desired goal of describing the non-linear stability behavior of the two-phase flow within a fuel assembly of a BWR will be achieved by the investigation of the time domain analysis of BWR instability (TOBI) model. This paper focuses on model-specific options and aspects of the POD-ROM methodology which are afterwards illustrated by means of a strongly non-linear dynamical system showing complex oscillating behavior.

Non‐linear Proper Orthogonal Decomposition Reduced Order Modeling: Bifurcation Study of a Natural Convection Circuit

AbstractBoiling water reactors (BWRs) not only show growing power oscillations at high‐power low‐flow conditions but also amplitude limited oscillations with temporal flow reversal. Methodologies, applicable in the non‐linear regime, allow insight into the physical mechanisms behind BWR dynamics. The present paper aims at a general non‐linear methodology capable to achieve reliable and numerical stable reduced order models (ROMs). Model‐specific options and prediction capabilities are adressed and illustrated by means of two strongly non‐linear dynamical systems: Firstly, the tubular reactor (TR), treated as a generic “pathologic” test case for perturbation investigations violating the inlet conditions, and secondly, the natural convection in a closed circuit (NCC), considered due to dynamical similarities to BWRs. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Active flutter suppression control law design method based on balanced proper orthogonal decomposition reduced order model

Active control for nonlinear aeroelastic structures is an attractive innovative technology. The design of classic active flutter controllers has often been based on low-fidelity and low-accuracy linear aerodynamic models. Multi-physics high-fidelity reduced order model (ROM) was used to design active control laws. In order to provide a lower-order model for controllers design, a balanced proper orthogonal decomposition ROM (POD-BT/ROM) was investigated. A state-space aeroservoelastic model and the active flutter suppression control law design method based on POD-BT/ROM were proposed. The effectiveness of the proposed method was then demonstrated by NACA 0012 airfoil, AGARD 445.6 wing and the Goland wing+ aeroelastic model.

A nonlinear POD reduced order model for limit cycle oscillation prediction

As the amplitude of the unsteady flow oscillation is large or large changes occur in the mean background flow such as limit cycle oscillation, the traditional proper orthogonal decomposition reduced order model based on linearized time or frequency domain small disturbance solvers can not capture the main nonlinear features. A new nonlinear reduced order model based on the dynamically nonlinear flow equation was investigated. The nonlinear second order snapshot equation in the time domain for proper orthogonal decomposition basis construction was obtained from the Taylor series expansion of the flow solver. The NLR 7301 airfoil configuration and Goland+ wing/store aeroelastic model were used to validate the capability and efficiency of the new nonlinear reduced order model. The simulation results indicate that the proposed new reduced order model can capture the limit cycle oscillation of aeroelastic system very well, while the traditional proper orthogonal decomposition reduced order model will lose effectiveness.