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Journal ArticleDOI

Adaptive matrix formation (AMF) method of space–time multigroup reactor kinetics equations in multidimensional model

01 Jan 2007-Annals of Nuclear Energy (ANNALS OF NUCLEAR ENERGY)-Vol. 34, Iss: 1, pp 103-119
TL;DR: Adaptive matrix formation (AMF) method has been developed for the numerical solution of the transient multigroup neutron diffusion and delayed precursor equations in two-and three-dimensional geometry.
About: This article is published in Annals of Nuclear Energy.The article was published on 2007-01-01. It has received 28 citations till now. The article focuses on the topics: Matrix (mathematics).
Citations
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01 Jan 2012
TL;DR: Nahla et al. as mentioned in this paper presented numerical techniques for processing the exponential function of the coefficient matrix using analytical method and fundamental matrix method, which were applied to three-dimensional space-time neutron diffusion equations with average one group of delayed neutrons in the different nuclear reactors.
Abstract: The space-time neutron diffusion equations with multi-group of delayed neutrons are a couple of the stiff nonlinear partial differential equations. The finite difference method is used to reduce the partial differential equations into ordinary differential equations. This ordinary differential equations are rewritten in a matrix form. The general solution of the matrix differential equation contains the exponential function of the coefficient matrix. The numerical techniques for processing the exponential function of the coefficient matrix are presented using analytical method and fundamental matrix method. The eigenvalues of the coefficient matrix are calculated numerically using FORTRAN computer code based on Laguerre’s method. The fundamental matrix and its inverse are calculated analytically for two energy groups of reactor kinetics and one group of precursor delayed neutrons. The numerical techniques are applied to three-dimensional space-time neutron diffusion equations with average one group of delayed neutrons in the different nuclear reactors. The results of numerical technique codes are compared with the results of traditional codes. ∗Corresponding author: Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt. 650 A. Nahla, F. Al-Malki and M. Rokaya

18 citations


Cites methods from "Adaptive matrix formation (AMF) met..."

  • ...This table substantiates that the thermal neutron flux of the NT-FMM and NT-AM are accurate comparing to the thermal neutron flux of the AMF....

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  • ...The thermal neutron flux of the NT-FMM and NT-AM is compared with the thermal neutron flux of 3DKIN and AMF....

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  • ...This table shows the results of the NT-FMM and NT-AM compared with the 3DKIN (Ferguson and Hanson, 1973[11]) and adaptive matrix formation, AMF (Aboanber and Nahla, 2007[3])....

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  • ...Adaptive Matrix Formation (AMF) method was presented and applied to homogeneous, symmetric heterogeneous and non-symmetric heterogeneous reactors in the case of two- and three-dimensions (Aboanber and Nahla, 2007)[3]....

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  • ...This table substantiates that the results of the NTFMM and NT-AM are an accurate comparing to the results of the AMF....

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Journal ArticleDOI
TL;DR: In this article, an analytical solution for point kinetics equations with one-group delayed neutron and extraneous neutron source is introduced to calculate the change of neutron density, which considers that the reactor does not reach steady state before a new reactivity is added.

14 citations

Journal ArticleDOI
TL;DR: The efficient computational system is presented to solve the neutron diffusion equations based on finite difference and theta methods and is considered a fast technique more than theta method and traditional numerical codes.

13 citations

Journal ArticleDOI
TL;DR: In this article, a novel analytical formulation is constructed and converged to high accuracy from the merger of the piecewise constant functions over a partition in time into the fundamental matrix for the two-energy group of the point kinetics equations.

11 citations

Journal ArticleDOI
TL;DR: In this article, an original methodology based on the Pade and Chebyshev rational approximations for the solution of the non-linear point kinetics equations with temperature reactivity feedback is described and investigated.

10 citations

References
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Book
30 Nov 1961
TL;DR: In this article, the authors propose Matrix Methods for Parabolic Partial Differential Equations (PPDE) and estimate of Acceleration Parameters, and derive the solution of Elliptic Difference Equations.
Abstract: Matrix Properties and Concepts.- Nonnegative Matrices.- Basic Iterative Methods and Comparison Theorems.- Successive Overrelaxation Iterative Methods.- Semi-Iterative Methods.- Derivation and Solution of Elliptic Difference Equations.- Alternating-Direction Implicit Iterative Methods.- Matrix Methods for Parabolic Partial Differential Equations.- Estimation of Acceleration Parameters.

5,317 citations

Book
01 Jan 1952
TL;DR: In this paper, the authors proposed a new approach for detecting NEUTRONS in the field of nuclear energy, based on the work of REACTEUR NUCLEAIRE.
Abstract: Keywords: REACTEUR NUCLEAIRE ; REACTEUR HOMOGENE ; ENERGIE NUCLEAIRE ; FISSION NUCLEAIRE ; NEUTRONS Note: Index Reference Record created on 2004-09-07, modified on 2016-08-08

433 citations

Journal ArticleDOI
TL;DR: In contrast with earlier nodal simulators, more recent nodal diffusion methods are characterized by the systematic derivation of spatial coupling relationships that are entirely consistent with the multigroup diffusion equation as discussed by the authors, which most often are derived by developing approximations to the one-dimensional equations obtained by integrating the multidimensional diffusion equation over directions transverse to each coordinate axis.

344 citations