عنوان مقاله [English]
نویسندگان [English]چکیده [English]
Nodal is a method for solving the neutron diffusion equation. It is categorized to analytic, semi-analytic and expansion nodal methods. In this research work, a software is developed in order to solve two group neutron diffusion equations in two dimensional Cartesian geometries. There are some approaches to the analytical solution of the neutron diffusion. An interesting approach, that is our recent concern, is the transverse leakage approximation. Based on this approximation, the two-dimensional diffusion equation is split into two one-dimensional equations and is solved analytically for each energy group. In this paper, we used flat and quadratic polynomials in order to approximate the transverse leakage terms. Finally, two reference problems are solved for verifying the proposed method. The results showed that the analytic nodal method with quadratic transverse leakage approximation gives very accurate results for the reactor core calculations.
 K.S. Smith, An analytic nodal method for solving the two group multidimensional static and transient neutron diffusion equations, PhD Thesis, MIT (1976).
 J.M. Aragones, C. Ahnert, N.G. Herranz, The analytic coarse mesh finite difference method for multi group and multidimensional diffusion calculations, Nuclear Science and Engineering, 157(1) (2007).
 H.G. Joo, D. Barber, G. Jiang, T.J. Downar, PARCS, A multi-dimensional two-group reactor kinetics code based on the nonlinear analytic nodal method, PU/NE-98-26 (1998).
 P.J. Turinsky, R.M.K. Al-Chalahi, P. Engrand, H.N. Sarsour, F.X. Faure, W. Guo, NESTLE: a few-group neutron diffusion equation solver utilizing the nodal expansion method for eigenvalue, adjoint, fixed-source steady-state and transient problems, EGG-NRE-11406 (1994).
 A. Trkov, Multi groups 3-dimensional neutron diffusion nodal code with thermo hydraulic feedbacks, Institute Jozef Stefan, Ljubljana, Slovenia, IJS-DP-6688, Rev. 2 (2008).
 Y.A. Chao, A theoretical analysis of the coarse mesh finite difference representation in advanced nodal methods, mathematics and computation, Reactor Physics and Environmental Analysis, in Nuclear Applications, (1) (1999) 117.
 N.G. Herranz, Analytic coarse-mesh finite-difference method generalized for heterogeneous multidimensional two group diffusion calculations, Nuclear Science and Engineering, 144 (2003) 23.
 A. Hebert, A simplified presentation of the multi groups analytic nodal method in 2D cartesian geometry, Annals of Nuclear Energy, 35 (2008) 2142.
 National energy software center: benchmark problem book, ANL-7416, Suppl. 1, 2, 3 (1985).