Integral formulation and numerical simulations for the neutron transport equation in X-Y geometry

被引：10

作者：

de Azevedo, F. S. ^{[1
]}

Sauter, E. ^{[1
]}

Konzen, P. H. A. ^{[1
]}

Thompson, M. ^{[1
]}

Barichello, L. B. ^{[1
]}

机构：

[1] Univ Fed Rio Grande do Sul, Inst Matemat & Estat, Programa Posgrad Matemat Aplicada, Av Bento Goncalves,POB 15080, Porto Alegre, RS, Brazil

来源：

ANNALS OF NUCLEAR ENERGY | 2018年 / 112卷

关键词：

Neutron transport theory; Integral formulation; Nystrom method; RADIATIVE HEAT-TRANSFER; APPROXIMATION; ALGORITHM; SPHERE; SLAB;

D O I：

10.1016/j.anucene.2017.10.017

中图分类号：

TL [原子能技术]; O571 [原子核物理学];

学科分类号：

0827 ; 082701 ;

摘要：

In this work the Nystrom method was used to solve the integral formulation of the neutron transport equation in X-Y geometry. Four quadrature schemes were tested, namely, Gauss-Legendre, GaussLobatto, Simpson, and Boole rules, for the numerical calculation of the integral formulation. Analytical techniques were used to remove singularities in order to accelerate the calculation scheme and to improve numerical accuracy. Explicit expressions were derived for evaluating relevant kernels. In addition to derive solutions for both fixed source and eigenvalue problems, the procedure provides pointwise solutions Where ray effects are mitigated leading to numerical results with high order accuracy for two dimensional scalar flux. Numerical results are listed with up to seven correct significant digits. (C) 2017 Elsevier Ltd. All rights reserved.

引用

页码：735 / 747

页数：13

共 50 条

[1] AN ITERATIVE METHOD FOR SOLVING NEUTRON TRANSPORT EQUATION IN X-Y GEOMETRY
DAVIS, JA
HAGEMAN, LA
[J]. SIAM JOURNAL ON APPLIED MATHEMATICS, 1969, 17 (01) : 149 - &
[2] Eigenvalues of the neutron transport equation in X-Y geometry and reflecting boundary conditions
de Azevedo, F. S.
Sauter, E.
Lorensi, G. A.
Mocellin, A. P. G.
[J]. PROGRESS IN NUCLEAR ENERGY, 2022, 144
[3] WALSH-FUNCTION APPROXIMATION FOR NEUTRON-TRANSPORT IN X-Y GEOMETRY
SEED, TJ
ALBRECHT, RW
[J]. TRANSACTIONS OF THE AMERICAN NUCLEAR SOCIETY, 1975, 21 (JUN): : 227 - 228
[4] COMPATIBLE PRODUCT ANGULAR QUADRATURE FOR NEUTRON-TRANSPORT IN X-Y GEOMETRY
ABUSHUMAYS, IK
[J]. NUCLEAR SCIENCE AND ENGINEERING, 1977, 64 (02) : 299 - 316
[5] A MULTIGROUP FINITE-ELEMENT SOLUTION OF THE NEUTRON-TRANSPORT EQUATION .1. X-Y GEOMETRY
WOOD, J
DEOLIVEIRA, C
[J]. ANNALS OF NUCLEAR ENERGY, 1984, 11 (05) : 229 - 243
[6] Element-free Galerkin modeling of neutron diffusion equation in X-Y geometry
Rokrok, B.
Minuchehr, H.
Zolfaghari, A.
[J]. ANNALS OF NUCLEAR ENERGY, 2012, 43 : 39 - 48
[7] DISCONTINUOUS FINITE-ELEMENT SOLUTIONS FOR NEUTRON-TRANSPORT IN X-Y GEOMETRY
ACKROYD, RT
ABUZID, OA
MIRZA, AM
[J]. ANNALS OF NUCLEAR ENERGY, 1995, 22 (3-4) : 181 - 201
[8] THE SPHERICAL-HARMONICS METHOD FOR THE MULTIGROUP TRANSPORT-EQUATION IN X-Y GEOMETRY
KOBAYASHI, K
OIGAWA, H
YAMAGATA, H
[J]. ANNALS OF NUCLEAR ENERGY, 1986, 13 (12) : 663 - 678
[9] Cellular neural network to the spherical harmonics approximation of neutron transport equation in x-y geometry Part II: Transient simulation
Pirouzmand, Ahmad
Hadad, Karnal
[J]. ANNALS OF NUCLEAR ENERGY, 2012, 47 : 225 - 233
[10] NUMERICAL-SOLUTIONS OF DISCRETE-ORDINATE NEUTRON-TRANSPORT EQUATIONS EQUIVALENT TO PL APPROXIMATION IN X-Y GEOMETRY
JUNG, J
OHTANI, N
KOBAYASH.K
NISHIHAR.H
[J]. JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY, 1974, 11 (06) : 231 - 241

← 1 2 3 4 5 →