Reed’s problem (William H. Reed (1971) New Difference Schemes for the Neutron Transport Equation, Nuclear Science and Engineering, 46:2, 309-314, DOI: 10.13182/NSE46-309) is a common test problem for transport codes. It is comprised of heterogeneous materials with strong absorber, vacuum, and scattering regions. These regions are valuable to testing different aspects of numerical discretizations.
PROBLEM neutron_sn DIM 1 GROUPS 1 SN $1
READ_MESH reed.msh
MATERIAL source1 S1=50 Sigma_t1=50 Sigma_s1.1=0
MATERIAL absorber S1=0 Sigma_t1=5 Sigma_s1.1=0
MATERIAL void S1=0 Sigma_t1=0 Sigma_s1.1=0
MATERIAL source2 S1=1 Sigma_t1=1 Sigma_s1.1=0.9
MATERIAL reflector S1=0 Sigma_t1=1 Sigma_s1.1=0.9
BC left mirror
BC right vacuum
SOLVE_PROBLEM
PRINT_FUNCTION phi1
$ gmsh -1 reed.geo
$ [...]
$ for n in 2 4 6 8; do feenox reed.fee ${n} | sort -g > reed-s${n}.csv; done
$
The solutions obtained in FeenoX with S_2, S_4, S_6 and S_8 are plotted and compared against and independent solution from https://www.drryanmc.com/solutions-to-reeds-problem/.