The Green's function method for effective multiplication benchmark calculations in multi-region slab geometry

The discrete ordinate method for angular flux calculations in slab geometry

“…Table 7 shows the effective multiplication factor of the multi-region slab geometry using GFM, PARTISN (PARallel TIme Dependent SN transport code (Alcouffe et al, 2000)) and DANT methods. The GFM (using Green's function and angular quadrature's) calculates integrals with error of 10badbreakafter−5 (Kornreich and Parsons, 2004). The DANT computations use an angular quadrature order of S 96 , and a convergence criterion of 10badbreakafter−8 (Alcouffe et al, 1995).…”

Time series analysis and Monte Carlo methods for eigenvalue separation in neutron multiplication problems

“…This type of problem would most likely be found in criticality safety work. The first four eigenvalue ratios of this problem (considered the benchmark) were computed using the Green's Function Method (GFM) [11] with a 1800-bin mesh across the entire domain and are shown in Table 1. The effective neutron multiplication factor ðk 0 Þ was calculated to be 0.424314 by GFM and 0.424314 ± 0.000007 by MC.…”

Contributions to solve the Multi-group Neutron Transport equation with different Angular Approaches

“…Several 1D and four 2D benchmarks were selected to test the methods. The 1D cases carried out are: first the ISSA benchmark found in various works like [Issa et al, 1986], [Deo et al, 2014], [Talaat],the second is the seven region a heterogeneous slab problem with 7 different regions from [Kornreich and Parsons, 2004] and others anisotropic problems until 6 energy groups have been performed from Sood et al [2003].…”

“…This problem is composed of seven slab regions with three different combinations of fuel, reflector and absorber [Kornreich and Parsons, 2004]. The one-energy group cross sections for these materials are shown in Table 3.2.…”