Discrete ordinates solutions of three-dimensional steady and transient neutron transport equations

Steady and a transient discrete ordinates neutron transport codes for three-dimensional geometry were developed based on the program DOT4.2. For the implementation of the time-dependence, a direct method, the fully implicit and unconditionally stable time integration scheme, was employed. The transient neutron transport equation was turned into the fixed-source neutron transport problem, and solved by the steady transport code for each time step. The two codes were tested with the TAKEDA benchmark and several transient benchmark problems. The numerical results show that the effective multiplication factors and regionwise neutron fluxes can be predicted accurately by the three-dimensional steady code with errors less than 0.1% and 4.0% respectively, for both delayed and prompt supercritical problems, the obtained results agree very well with the benchmark problem ones.