A Reduced Order Model for Multi-Group Time-Dependent Parametrized Reactor Spatial Kinetics

2014 ◽  
Author(s):  
Alberto Sartori ◽  
Davide Baroli ◽  
Antonio Cammi ◽  
Lelio Luzzi ◽  
Gianluigi Rozza
Keyword(s):  
Reduced Order Model ◽  
Time Dependent ◽  
Element Approximation ◽  
Fissile Material ◽  
Spatial Effects ◽  
Reduced Basis ◽  
Order Model ◽  
Control Rod ◽  
Reduced Order ◽  
Group Time

In this work, a Reduced Order Model (ROM) for multi-group time-dependent parametrized reactor spatial kinetics is presented. The Reduced Basis method (built upon a high-fidelity “truth” finite element approximation) has been applied to model the neutronics behavior of a parametrized system composed by a control rod surrounded by fissile material. The neutron kinetics has been described by means of a parametrized multi-group diffusion equation where the height of the control rod (i.e., how much the rod is inserted) plays the role of the varying parameter. In order to model a continuous movement of the rod, a piecewise affine transformation based on subdomain division has been implemented. The proposed ROM is capable to efficiently reproduce the neutron flux distribution allowing to take into account the spatial effects induced by the movement of the control rod with a computational speed-up of 30000 times, with respect to the “truth” model.

scholarly journals POD-Galerkin reduced order methods for CFD using Finite Volume Discretisation: vortex shedding around a circular cylinder

2017 ◽  
Vol 8 (1) ◽  
pp. 210-236 ◽  
Author(s):  
Giovanni Stabile ◽  
Saddam Hijazi ◽  
Andrea Mola ◽  
Stefano Lorenzi ◽  
Gianluigi Rozza
Keyword(s):  
Circular Cylinder ◽  
Finite Volume ◽  
Vortex Shedding ◽  
Dimensional Space ◽  
Reduced Order Model ◽  
Galerkin Projection ◽  
Governing Equations ◽  
Reduced Basis ◽  
Order Model ◽  
Reduced Order

Abstract Vortex shedding around circular cylinders is a well known and studied phenomenon that appears in many engineering fields. A Reduced Order Model (ROM) of the incompressible ow around a circular cylinder is presented in this work. The ROM is built performing a Galerkin projection of the governing equations onto a lower dimensional space. The reduced basis space is generated using a Proper Orthogonal Decomposition (POD) approach. In particular the focus is into (i) the correct reproduction of the pres- sure field, that in case of the vortex shedding phenomenon, is of primary importance for the calculation of the drag and lift coefficients; (ii) the projection of the Governing equations (momentum equation and Poisson equation for pressure) performed onto different reduced basis space for velocity and pressure, respectively; (iii) all the relevant modifications necessary to adapt standard finite element POD-Galerkin methods to a finite volume framework. The accuracy of the reduced order model is assessed against full order results.

In-Plane Stretching in MEMS Actuated Deformable Mirrors

2006 ◽  
Author(s):  
Vineel Mallela ◽  
John Zhe ◽  
D. Dane Quinn
Keyword(s):  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Reduced Order Model ◽  
Time Dependent ◽  
Deformable Mirror ◽  
Discrete Elements ◽  
Order Model ◽  
Reduced Order ◽  
Mems Actuators ◽  
Geometrically Exact Shell

We consider the response of a continuously deformable mirror with discrete MEMS actuators. The mirror itself is described with a geometrically exact shell model incorporating both flexural and extensional strains, while the MEMS actuators are represented as discrete elements subject to a time-dependent voltage. A reduced-order model is developed through a Galerkin reduction and the resulting equations are subjected to the method of multiple scales. The response of the system is then analyzed to uncover the ability of the system follow desired mirror profiles.

scholarly journals Geometrically nonlinear autonomous reduced order model for rotating structures

2018 ◽  
Author(s):  
Mikel Balmaseda ◽  
Georges Jacquet-Richardet ◽  
Antoine Placzek ◽  
Duc-Minh Tran
Keyword(s):  
Normal Modes ◽  
Harmonic Balance Method ◽  
Reduced Order Model ◽  
Static Equilibrium ◽  
Evaluation Procedure ◽  
Element Formulation ◽  
Geometrically Nonlinear ◽  
Reduced Basis ◽  
Order Model ◽  
Reduced Order

In the present work, as an extension to [2], an autonomous geometrically nonlinear reduced order model for the study of dynamic solutions of complex rotating structures is developed. In opposition to the classical finite element formulation for geometrically nonlinear rotating structures that considers small linear vibrations around the static equilibrium, nonlinear vibrations around the pre-stressed equilibrium are now considered. For that purpose, the linear normal modes are used as a reduced basis for the construction of the reduced order model. The stiffness evaluation procedure method (STEP) [4] is applied to compute the nonlinear forces induced by the displacements around the static equilibrium. This approach enhances the classical linearised small perturbations hypothesis to the cases of large displacements around the static pre-stressed equilibrium. Furthermore, a comparison between the steady solution given by HHT-α [1] and the Harmonic Balance Method (HBM) [3] is carried out. The proposed reduced order models are evaluated for a rotating beam case study.

scholarly journals Time Stable Reduced Order Modeling by an Enhanced Reduced Order Basis of the Turbulent and Incompressible 3D Navier–Stokes Equations

2019 ◽  
Vol 24 (2) ◽  
pp. 45 ◽  
Author(s):  
Nissrine Akkari ◽  
Fabien Casenave ◽  
Vincent Moureau
Keyword(s):  
Stokes Equations ◽  
A Priori ◽  
Order Reduction ◽  
Reduced Order Modeling ◽  
Reduced Order Model ◽  
Navier Stokes ◽  
Reduced Basis ◽  
Order Model ◽  
Navier Stokes Equations ◽  
Reduced Order

In the following paper, we consider the problem of constructing a time stable reduced order model of the 3D turbulent and incompressible Navier–Stokes equations. The lack of stability associated with the order reduction methods of the Navier–Stokes equations is a well-known problem and, in general, it is very difficult to account for different scales of a turbulent flow in the same reduced space. To remedy this problem, we propose a new stabilization technique based on an a priori enrichment of the classical proper orthogonal decomposition (POD) modes with dissipative modes associated with the gradient of the velocity fields. The main idea is to be able to do an a priori analysis of different modes in order to arrange a POD basis in a different way, which is defined by the enforcement of the energetic dissipative modes within the first orders of the reduced order basis. This enables us to model the production and the dissipation of the turbulent kinetic energy (TKE) in a separate fashion within the high ranked new velocity modes, hence to ensure good stability of the reduced order model. We show the importance of this a priori enrichment of the reduced basis, on a typical aeronautical injector with Reynolds number of 45,000. We demonstrate the capacity of this order reduction technique to recover large scale features for very long integration times (25 ms in our case). Moreover, the reduced order modeling (ROM) exhibits periodic fluctuations with a period of 2 . 2 ms corresponding to the time scale of the precessing vortex core (PVC) associated with this test case. We will end this paper by giving some prospects on the use of this stable reduced model in order to perform time extrapolation, that could be a strategy to study the limit cycle of the PVC.

Application of a Reduced Order Model for Fuzzy Analysis of Linear Static Systems

2021 ◽  
Vol 7 (2) ◽  
Author(s):  
Marcos A. Valdebenito ◽  
Héctor A. Jensen ◽  
Pengfei Wei ◽  
Michael Beer ◽  
André T. Beck
Keyword(s):  
Dimensional Space ◽  
Reduced Order Model ◽  
Optimization Strategy ◽  
Reduced Basis ◽  
Order Model ◽  
Full System ◽  
Reduced Order ◽  
Fuzzy Analysis ◽  
Α Level ◽  
Static Systems

Abstract This contribution proposes a strategy for performing fuzzy analysis of linear static systems applying α-level optimization. In order to decrease numerical costs, full system analyses are replaced by a reduced order model that projects the equilibrium equations to a small-dimensional space. The basis associated with the reduced order model is constructed by means of a single analysis of the system plus a sensitivity analysis. This reduced basis is enriched as the α-level optimization strategy progresses in order to protect the quality of the approximations provided by the reduced order model. A numerical example shows that with the proposed strategy, it is possible to produce an accurate estimate of the membership function of the response of the system with a limited number of full system analyses.

Sign in / Sign up

Export Citation Format

Share Document