scholarly journals Reduced-Order Modelling with Domain Decomposition Applied to Multi-Group Neutron Transport

Energies ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1369
Author(s):  
Toby R. F. Phillips ◽  
Claire E. Heaney ◽  
Brendan S. Tollit ◽  
Paul N. Smith ◽  
Christopher C. Pain
Keyword(s):  
Domain Decomposition ◽  
Neutron Transport ◽  
Computational Cost ◽  
Basis Functions ◽  
Reduced Order Model ◽  
Test Case ◽  
Order Model ◽  
Reduced Order ◽  
Reduced Order Modelling ◽  
Neutron Transport Equations

Solving the neutron transport equations is a demanding computational challenge. This paper combines reduced-order modelling with domain decomposition to develop an approach that can tackle such problems. The idea is to decompose the domain of a reactor, form basis functions locally in each sub-domain and construct a reduced-order model from this. Several different ways of constructing the basis functions for local sub-domains are proposed, and a comparison is given with a reduced-order model that is formed globally. A relatively simple one-dimensional slab reactor provides a test case with which to investigate the capabilities of the proposed methods. The results show that domain decomposition reduced-order model methods perform comparably with the global reduced-order model when the total number of reduced variables in the system is the same with the potential for the offline computational cost to be significantly less expensive.

scholarly journals Multi-fidelity non-intrusive reduced-order modelling based on manifold alignment

2021 ◽  
Vol 477 (2253) ◽  
pp. 20210495
Author(s):  
Christian Perron ◽  
Dushhyanth Rajaram ◽  
Dimitri N. Mavris
Keyword(s):  
Predictive Accuracy ◽  
Computational Cost ◽  
Predictive Performance ◽  
Reduced Order Model ◽  
Training Data ◽  
Order Model ◽  
Reduced Order ◽  
Reduced Order Modelling ◽  
Manifold Alignment ◽  
Computational Budget

This work presents the development of a multi-fidelity, parametric and non-intrusive reduced-order modelling method to tackle the problem of achieving an acceptable predictive accuracy under a limited computational budget, i.e. with expensive simulations and sparse training data. Traditional multi-fidelity surrogate models that predict scalar quantities address this issue by leveraging auxiliary data generated by a computationally cheaper lower fidelity code. However, for the prediction of field quantities, simulations of different fidelities may produce responses with inconsistent representations, rendering the direct application of common multi-fidelity techniques challenging. The proposed approach uses manifold alignment to fuse inconsistent fields from high- and low-fidelity simulations by individually projecting their solution onto a common latent space. Hence, simulations using incompatible grids or geometries can be combined into a single multi-fidelity reduced-order model without additional manipulation of the data. This method is applied to a variety of multi-fidelity scenarios using a transonic airfoil problem. In most cases, the new multi-fidelity reduced-order model achieves comparable predictive accuracy at a lower computational cost. Furthermore, it is demonstrated that the proposed method can combine disparate fields without any adverse effect on predictive performance.

scholarly journals Reduced Order Model of Position Control System

2011 ◽  
pp. 113-115
Author(s):  
Yogesh V. Hote ◽  
A. N. Jha ◽  
J. R. P. Gupta
Keyword(s):  
Control System ◽  
Position Control ◽  
Open Loop ◽  
Simple Approach ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Reduced Order Modelling ◽  
Position Control System

In this paper, simple approach is proposed to determine reduced order model of a unstable open-loop position control system. This approach is based on Krishnamurthy’s approach on Routh criterion on reduced order modelling. The results are simulated in Matlab environment.

A POD reduced-order model for resolving the neutron transport problems of nuclear reactor

2020 ◽  
Vol 149 ◽  
pp. 107799
Author(s):  
Yue Sun ◽  
Junhe Yang ◽  
Yahui Wang ◽  
Zhuo Li ◽  
Yu Ma
Keyword(s):  
Nuclear Reactor ◽  
Neutron Transport ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Transport Problems

scholarly journals A domain decomposition non-intrusive reduced order model for turbulent flows

2019 ◽  
Vol 182 ◽  
pp. 15-27 ◽  
Author(s):  
D. Xiao ◽  
C.E. Heaney ◽  
F. Fang ◽  
L. Mottet ◽  
R. Hu ◽  
...  
Keyword(s):  
Domain Decomposition ◽  
Turbulent Flows ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order

scholarly journals A Comprehensive CFD Model for Dual-Phase Brass Indirect Extrusion Based on Constitutive Laws: Assessment of Hot-Zone Formation and Failure Prognosis

Metals ◽  
2018 ◽  
Vol 8 (12) ◽  
pp. 1043 ◽  
Author(s):  
George Pashos ◽  
George Pantazopoulos ◽  
Ioannis Contopoulos
Keyword(s):  
Stokes Equations ◽  
Metal Flow ◽  
Computational Cost ◽  
Constitutive Laws ◽  
Reduced Order Model ◽  
Preliminary Evaluation ◽  
Order Model ◽  
Zone Formation ◽  
Reduced Order ◽  
Prediction And Prevention

A numerical method for the precise calculation of temperature, velocity and pressure profiles of the α-β brass indirect hot extrusion process is presented. The method solves the Navier–Stokes equations for non-Newtonian liquids with strain-rate and temperature-dependent viscosity that is formulated using established constitutive laws based on the Zener–Hollomon type equation for plastic flow stress. The method can be implemented with standard computational fluid dynamics (CFD) software, has relatively low computational cost, and avoids the numerical artifacts associated with other methods commonly used for such processes. A response surface technique is also implemented, and it is thus possible to build a reduced order model that approximately maps the process with respect to all combinations of its parameters, including the extrusion speed and brass phase constitution. The reduced order model can be a very useful tool for production, because it instantaneously provides important quantities, such as the average pressure or the temperature of hot-spots that are formed due to the combined effect of die/billet friction and the generation of heat from plastic deformation (adiabatic shear deformation heating). This approach can assist in the preliminary evaluation of the metal flow pattern, and in the prediction and prevention of critical extrusion failures, thus leading to subsequent process and product quality improvements.

Computationally Efficient Approaches to Simulate the Dynamics of Microbeams Under Mechanical Shock

2006 ◽  
Author(s):  
Mohammad I. Younis ◽  
Danial Jordy ◽  
James M. Pitarresi
Keyword(s):  
Hybrid Approach ◽  
Computational Cost ◽  
Nonlinear Behavior ◽  
Reduced Order Model ◽  
Beam Model ◽  
Mechanical Shock ◽  
Computationally Efficient ◽  
Order Model ◽  
Reduced Order ◽  
Dynamic Loading Conditions

We present computationally efficient models and approaches and utilize them to investigate the dynamics of microbeams under mechanical shock. We explore using a hybrid approach utilizing a beam model combined with the shock spectrum of a spring-mass-damper model. We conclude that this approach is computationally efficient and yields accurate results in both quasi-static and dynamic loading conditions. We utilize a reduced-order model based on the nonlinear Euler-Bernoulli beam model. We demonstrate that this model is capable of capturing accurately the dynamic behavior of microbeams under shock pulses of various amplitudes (low-g and high-g), in various damping conditions, structural boundaries (clamped-clamped and clamped-free), and can capture both linear and nonlinear behavior. We investigate high-g loading cases. We report significant increase in the computational cost of simulations when using traditional nonlinear finite-element models because of the activation of higher-order modes. We demonstrate that the developed reduced-order model can be very efficient in such cases.

Inverse Determination of Moving Heat Flux Distributions Using Reduced Order Models

2014 ◽  
Author(s):  
Brian H. Dennis ◽  
Ashkan Akbariyeh ◽  
John Michopoulos ◽  
Foteini Komninelli ◽  
Athanasios Iliopoulos
Keyword(s):  
Heat Flux ◽  
Finite Element ◽  
Finite Element Model ◽  
Target Surface ◽  
Element Model ◽  
Basis Functions ◽  
Reduced Order Model ◽  
Analysis Model ◽  
Order Model ◽  
Reduced Order

Optimization-based solutions to inverse problems involve the coupling of an analysis model, such as a finite element model, with a numerical optimization method. The goal is to determine a set of parameters that minimize an objective function that is determined by solving the analysis model. In this paper, we present an approach that dramatically reduces the computational cost for solving this inverse problems in this way by replacing the original full order finite element model (FOM) with a reduced order model (ROM) that is both accurate and quick to compute. The reduced order model is constructed with basis functions generated using proper orthogonal decomposition of set of solutions from the FOM. A discrete Galerkin method is used to project the differential equation on the basis functions. This approach allows us to transform the linear full order finite element model into an equivalent discrete ROM with far fewer unknowns. The method is applied to a parameter estimation problem in heat transfer. Specifically, we determine the parameters governing the magnitude and distribution of an unknown surface heat flux moving at a constant velocity across the surface of a solid bar of material. A finite element model was implemented in the commercial package COMSOL and a corresponding ROM was constructed. The ROM was coupled with an optimization algorithm to determine the parameter values that minimized the distance between the computed surface temperatures and the target surface temperature. The target surface temperature was generated using simulated measurements produced from the full order finite element model. Several optimization methods were used. The results show the approach can recover the parameters with high accuracy with twenty seven FOM runs.

scholarly journals Proper Orthogonal Decomposition-Based Method for Predicting Flow and Heat Transfer of Oil and Water in Reservoir

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
Xianhang Sun ◽  
Bingfan Li ◽  
Xu Ma ◽  
Yi Pan ◽  
Shuangchun Yang ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Proper Orthogonal Decomposition ◽  
Orthogonal Decomposition ◽  
Basis Functions ◽  
Hot Water ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Flow And Heat Transfer ◽  
Proper Orthogonal

Calculation process of some reservoir engineering problems involves several passes of full-order numerical reservoir simulations, and this makes it a time-consuming process. In this study, a fast method based on proper orthogonal decomposition (POD) was developed to predict flow and heat transfer of oil and water in a reservoir. The reduced order model for flow and heat transfer of oil and water in the hot water-drive reservoir was generated. Then, POD was used to extract a reduced set of POD basis functions from a series of “snapshots” obtained by a finite difference method (FDM), and these POD basis functions most efficiently represent the dynamic characteristics of the original physical system. After injection and production parameters are changed constantly, the POD basis functions combined with the reduced order model were used to predict the new physical fields. The POD-based method was approved on a two-dimensional hot water-drive reservoir model. For the example of this paper, compared with FDM, the prediction error of water saturation and temperature fields were less than 1.3% and 1.5%, respectively; what is more, it was quite fast, where the increase in calculation speed was more than 70 times.

scholarly journals Development of a Reduced Order Model for Fuel Burnup Analysis

Energies ◽  
2020 ◽  
Vol 13 (4) ◽  
pp. 890 ◽  
Author(s):  
Christian Castagna ◽  
Manuele Aufiero ◽  
Stefano Lorenzi ◽  
Guglielmo Lomonaco ◽  
Antonio Cammi
Keyword(s):  
Methodological Approach ◽  
Computational Cost ◽  
Reaction Rates ◽  
Reduced Order Model ◽  
Fuel Burnup ◽  
Order Model ◽  
Reduced Order ◽  
Solution Accuracy ◽  
Proper Orthogonal ◽  
Over Time

Fuel burnup analysis requires a high computational cost for full core calculations, due to the amount of the information processed for the total reaction rates in many burnup regions. Indeed, they reach the order of millions or more by a subdivision into radial and axial regions in a pin-by-pin description. In addition, if multi-physics approaches are adopted to consider the effects of temperature and density fields on fuel consumption, the computational load grows further. In this way, the need to find a compromise between computational cost and solution accuracy is a crucial issue in burnup analysis. To overcome this problem, the present work aims to develop a methodological approach to implement a Reduced Order Model (ROM), based on Proper Orthogonal Decomposition (POD), in fuel burnup analysis. We verify the approach on 4 years of burnup of the TMI-1 unit cell benchmark, by reconstructing fuel materials and burnup matrices over time with different levels of approximation. The results show that the modeling approach is able to reproduce reactivity and nuclide densities over time, where the accuracy increases with the number of basis functions employed.

A Reduced-Order Model for Turbomachinery Flows Using Proper Orthogonal Decomposition

2013 ◽  
Author(s):  
Thomas A. Brenner ◽  
Forrest L. Carpenter ◽  
Brian A. Freno ◽  
Paul G. A. Cizmas
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Stokes Equations ◽  
Computational Cost ◽  
Wheel Speed ◽  
Orthogonal Decomposition ◽  
Reduced Order Model ◽  
Computational Time ◽  
Order Model ◽  
Reduced Order ◽  
Proper Orthogonal

This paper presents the development of a reduced-order model based on the proper orthogonal decomposition (POD) method. The POD method has been developed to predict turbomachinery flows modeled by the Reynolds-averaged Navier–Stokes equations. The purpose of using a POD-based reduced-order model is to decrease the computational cost of turbomachinery flows. The POD model has been tested for two configurations: a canonical channel with a bump case and the transonic NASA Rotor 67 case. The Rotor 67 case has been simulated at design wheel speed and at three off-design conditions: 70, 80, and 90% of the wheel speed. The results of the POD-based reduced-order model where in excellent agreement with the full-order model results. The computational time of the reduced-order model was approximately one order of magnitude smaller than that of the full-order model.

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