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galerkin-finite-element-method
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Sensitivity analysis of the galerkin finite element method neutron diffusion solver to the shape of the elements
, Article Nuclear Engineering and Technology ; Volume 49, Issue 1 , 2017 , Pages 29-42 ; 17385733 (ISSN) ; Sharif University of Technology
Korean Nuclear Society
2017
Abstract
The purpose of the present study is the presentation of the appropriate element and shape function in the solution of the neutron diffusion equation in two-dimensional (2D) geometries. To this end, the multigroup neutron diffusion equation is solved using the Galerkin finite element method in both rectangular and hexagonal reactor cores. The spatial discretization of the equation is performed using unstructured triangular and quadrilateral finite elements. Calculations are performed using both linear and quadratic approximations of shape function in the Galerkin finite element method, based on which results are compared. Using the power iteration method, the neutron flux distributions with...
3D neutron diffusion computational code based on GFEM with unstructured tetrahedron elements: A comparative study for linear and quadratic approximations
, Article Progress in Nuclear Energy ; Volume 92 , 2016 , Pages 119-132 ; 01491970 (ISSN) ; Sharif University of Technology
Elsevier Ltd
2016
Abstract
In the present study, the comparison between the results obtained from the linear and quadratic approximations of the Galerkin Finite Element Method (GFEM) for neutronic reactor core calculation was reported. The sensitivity analysis of the calculated neutron multiplication factor, neutron flux and power distributions in the reactor core vs. the number of the unstructured tetrahedron elements and order of the considered shape function was performed. The cost of the performed calculation using linear and quadratic approximation was compared through the calculation of the FOM. The neutronic core calculation was performed for both rectangular and hexagonal geometries. Both the criticality and...
Electromagnetic Wave Propagation Analysis Using Level Set Method
, M.Sc. Thesis Sharif University of Technology ; Shishegar, Amir Ahmad (Supervisor)
Abstract
Always, there has been a great interest toward electromagnetic wave propagation and new ways for simulation of the problem. Level set methods provide a powerful mathematical framework for propagating surfaces (in 3-D) or curves (in 2-D). The contours of the moving objects are viewed as the zero level sets of a function and propagated in a Eulerian point of view by means of a Hamilton–Jacobi partial differential equation expressing the conservation of the level sets under a given velocity field. Level set methods have been applied in a wide range of domains, such as physics, chemistry, fluid dynamics, combustion, image processing… In this thesis, we introduce a new numerical procedure for...
Compositional Simulation of Reservoirs Using Finite Element Method
, M.Sc. Thesis Sharif University of Technology ; Pishvaie, Mahmoud Reza (Supervisor) ; Mobin, Fatemi (Supervisor)
Abstract
One of the main purposes of this study is to present a robust and yet efficient semi-discretized algorithm for compositional simulation. All the equations including both the mass balance and the phase equilibrium equations are solved simultaneously which forms a Differential-Algebraic set of Equations and is solved by utilizing an efficient MATLAB solver. Furthermore, another formulation and algorithm is proposed which is consisted of two sets of equations, the primary equations (differential mass balance equations) and the secondary equations (the algebraic phase equilibrium equations). The gradient terms in the primary equations are discretized by using finite element method (Galerkin...
On a various noise source reconstruction algorithms in VVER-1000 reactor core
, Article Nuclear Engineering and Design ; Volume 261 , 2013 , Pages 132-143 ; 00295493 (ISSN) ; Vosoughi, N ; Sharif University of Technology
2013
Abstract
In present study, the neutron noise source is reconstructed using three different unfolding techniques in a typical VVER-1000 reactor core. In first stage, the neutron noise calculation based on Galerkin finite element method (GFEM) is performed; in which the neutron noise in two energy group due to the noise sources of type absorber of variable strength and vibrating absorber is calculated. The neutron noise due to inadvertent loading of a fuel assembly in an improper position (ILFAIP), as a new defined noise source in the neutron noise studies, is calculated as well. In the second stage, the inversion, zoning and scanning methods are applied for reconstruction of the noise source of type...
Development of 3D neutron noise simulator based on GFEM with unstructured tetrahedron elements
, Article Annals of Nuclear Energy ; Volume 97 , 2016 , Pages 132-141 ; 03064549 (ISSN) ; Vosoughi, N ; Sharif University of Technology
Elsevier Ltd
Abstract
In the present study, the neutron noise, i.e. the stationary fluctuation of the neutron flux around its mean value is calculated based on the 2G, 3D neutron diffusion theory. To this end, the static neutron calculation is performed at the first stage. The spatial discretization of the neutron diffusion equation is performed based on linear approximation of Galerkin Finite Element Method (GFEM) using unstructured tetrahedron elements. Using power iteration method, neutron flux and corresponding eigen-value are obtained. The results are then benchmarked against the valid results for VVER-1000 (3D) benchmark problem. In the second stage, the neutron noise equation is solved using GFEM and...
, Ph.D. Dissertation Sharif University of Technology ; Vosoughi, Naser (Supervisor)
Abstract
The present ph.D. thesis consists of three sections including the static calculation, neutron noise calculation and neutron noise source unfolding in VVER-1000 reactor core. The multi-group, two dimensional neutron diffusion equations and corresponding adjoint equations are solved in the static calculation. The spatial discretization of equations is based on Galerkin Finite Element Method (GFEM) using unstructured triangle elements generated by Gambit software. The static calculation is performed for both linear and quadratic approximations of shape function; baesd on which results are compared. Using power iteration method for the static calculation, the neutron and adjoint fluxes with the...
Noise source reconstruction using ANN and hybrid methods in VVER-1000 reactor core
, Article Progress in Nuclear Energy ; Vol. 71, issue , 2014 , pp. 232-247 ; ISSN: 01491970 ; Vosoughi, N ; Sharif University of Technology
Abstract
The present paper consists of two separate sections. In the first section, the neutron noise source is reconstructed using Artificial Neural Network (ANN) in a typical VVER-1000 reactor core. In the first stage of this section, the neutron noise calculations are performed based on Galerkin Finite Element Method (GFEM). To this end, two types of noise sources including absorber of variable strength and vibrating absorber are considered. As the results of noise calculations, the neutron noise is obtained in the location of detectors. In the second stage, the multilayer perception neural network is developed for reconstruction of the noise source. Complex neutron noises (real and imaginary...
Neutron noise simulation by GFEM and unstructured triangle elements
, Article Nuclear Engineering and Design ; Volume 253 , 2012 , Pages 238-258 ; 00295493 (ISSN) ; Vosoughi, N ; Sharif University of Technology
2012
Abstract
In the present study, the neutron noise, i.e. The stationary fluctuation of the neutron flux around its mean value, is calculated in 2-group forward and adjoint diffusion theory for both hexagonal and rectangular reactor cores. To this end, the static neutron calculation is performed at the first stage. The spatial discretization of equations is based on linear approximation of Galerkin Finite Element Method (GFEM) using unstructured triangle elements. Using power iteration method, forward and adjoint fluxes with the corresponding eigenvalues are obtained. The results are then benchmarked against the valid results for BIBLIS-2D and IAEA-2D benchmark problems and DONJON computer code. The...
A Petrov-Galerkin finite element method using polyfractonomials to solve stochastic fractional differential equations
, Article Applied Numerical Mathematics ; Volume 169 , 2021 , Pages 64-86 ; 01689274 (ISSN) ; Foroush Bastani, A ; Zohouri Zangeneh, B ; Sharif University of Technology
Elsevier B.V
2021
Abstract
In this paper, we are concerned with existence, uniqueness and numerical approximation of the solution process to an initial value problem for stochastic fractional differential equation of Riemann-Liouville type. We propose and analyze a Petrov-Galerkin finite element method based on fractional (non-polynomial) Jacobi polyfractonomials as basis and test functions. Error estimates in L2 norm are derived and numerical experiments are provided to validate the theoretical results. As an illustrative application, we generate sample paths of the Riemann-Liouville fractional Brownian motion which is of importance in many applications ranging from geophysics to traffic flow in telecommunication...
A Petrov-Galerkin finite element method using polyfractonomials to solve stochastic fractional differential equations
, Article Applied Numerical Mathematics ; Volume 169 , 2021 , Pages 64-86 ; 01689274 (ISSN) ; Foroush Bastani, A ; Zohouri Zangeneh, B ; Sharif University of Technology
Elsevier B.V
2021
Abstract
In this paper, we are concerned with existence, uniqueness and numerical approximation of the solution process to an initial value problem for stochastic fractional differential equation of Riemann-Liouville type. We propose and analyze a Petrov-Galerkin finite element method based on fractional (non-polynomial) Jacobi polyfractonomials as basis and test functions. Error estimates in L2 norm are derived and numerical experiments are provided to validate the theoretical results. As an illustrative application, we generate sample paths of the Riemann-Liouville fractional Brownian motion which is of importance in many applications ranging from geophysics to traffic flow in telecommunication...
A sequential implicit discrete fracture model for three-dimensional coupled flow-geomechanics problems in naturally fractured porous media
, Article Journal of Petroleum Science and Engineering ; Volume 150 , 2017 , Pages 312-322 ; 09204105 (ISSN) ; Shamloo, A ; Dezfuli, A. D ; Sharif University of Technology
Abstract
A sequential implicit numerical method based on discrete-fracture model and the Galerkin Finite Element method, for time-dependent coupled fluid flow and geomechanics problems in fractured subsurface formations is presented. Discrete-fracture model has been used to explicitly represent the fracture network inside porous media. The Galerkin Finite Element method with adaptive unstructured gridding is implemented to numerically solve the spatially three-dimensional and time-dependent problem. The presented method is validated with previously obtained solutions. Two problems are numerically solved by applying the presented methodology in a three-dimensional fractured petroleum reservoir under...
On a various soft computing algorithms for reconstruction of the neutron noise source in the nuclear reactor cores
, Article Annals of Nuclear Energy ; Volume 114 , 2018 , Pages 19-31 ; 03064549 (ISSN) ; Esmaili Paeen Afrakoti, I ; Sharif University of Technology
Elsevier Ltd
2018
Abstract
This paper presents a comparative study of various soft computing algorithms for reconstruction of neutron noise sources in the nuclear reactor cores. To this end, the computational code for reconstruction of neutron noise source is developed based on the Adaptive Neuro-Fuzzy Inference System (ANFIS), Decision Tree (DT), Radial Basis Function (RBF) and Support Vector Machine (SVM) algorithms. Neutron noise source reconstruction process using the developed computational code consists of three stages of training, testing and validation. The information of neutron noise sources and induced neutron noise distributions are used as output and input data of training stage, respectively. As input...