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

[21] THERMOGENE, AN INTEGRAL TRANSPORT PROGRAM FOR ARBITRARY X-Y GEOMETRY SYSTEMS .1. BASIC THEORY OF PROGRAM AND CALCULATED RESULTS
JANSSEN, AJ
CASPERS, LM
[J]. ATOMKERNENERGIE, 1973, 21 (01): : 27 - 35
[22] ACCELERATION METHOD FOR NODAL EQUATION OF DIFFUSION EQUATION IN X-Y GEOMETRY DERIVED BY FINITE FOURIER TRANSFORMATION
HIYAMA, N
KOBAYASHI, K
[J]. JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY, 1991, 28 (01) : 1 - 13
[23] Cellular neural network to the spherical harmonics approximation of neutron transport equation in x-y geometry. Part I: Modeling and verification for time-independent solution
Pirouzmand, Ahmad
Hadad, Kamal
[J]. ANNALS OF NUCLEAR ENERGY, 2011, 38 (06) : 1288 - 1299
[24] A NUMERICAL METHOD FOR SOLVING NEUTRON TRANSPORT EQUATION IN FINITE CYLINDRICAL GEOMETRY
TAKEUCHI, K
[J]. JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY-TOKYO, 1969, 6 (08): : 466 - &
[25] Solution of the neutron moderation equation in x,y geometry by the splitting method
Platonov, AP
[J]. ATOMIC ENERGY, 1998, 84 (03) : 160 - 162
[26] Solution of the neutron moderation equation in x, y geometry by the splitting method
A. P. Platonov
[J]. Atomic Energy, 1998, 84 : 160 - 162
[27] THERMOGENE, AN INTEGRAL TRANSPORT PROGRAM FOR ARBITRARY X-Y GEOMETRY SYSTEMS .3. CALCULATION OF ACTUAL LIGHT WATER REACTOR LATTICES
JANSSEN, AJ
BRAND, P
CASPERS, LM
[J]. ATOMKERNENERGIE, 1973, 22 (01): : 14 - 23
[28] DISCRETE ORDINATES NUMERICAL INTEGRATION METHOD FOR NEUTRON TRANSPORT EQUATION IN SLAB GEOMETRY
TAKEUCHI, K
KATAOKA, I
[J]. JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY-TOKYO, 1968, 5 (07): : 342 - &
[29] THERMOGENE, AN INTEGRAL TRANSPORT PROGRAM FOR ARBITRARY X-Y GEOMETRY SYSTEMS - 3. CALCULATION OF ACTUAL LIGHT WATER REACTOR LATTICES.
Janssen, A.J.
Brand, P.
Caspers, L.M.
[J]. 1600, (22):
[30] SOLUTION OF STANDARD DIAMOND DIFFERENCE EQUATIONS FOR DISCRETE-ORDINATE NEUTRON-TRANSPORT EQUATIONS EQUIVALENT TO PL APPROXIMATION IN X-Y GEOMETRY
JUNG, J
OHTANI, N
KOBAYASHI, K
NISHIHARA, H
[J]. NUCLEAR SCIENCE AND ENGINEERING, 1974, 53 (04) : 355 - 369

← 1 2 3 4 5 →