The simulation of the neutron diffusion equations over many decades

This paper describes the simulation of a nuclear re actor system using the neutron diffusion equations coupled to the thermodynamic and mechanical equations. In this coupling, representation of the diffusion equation presents considerable difficulty when large power excursions are being simulated. This difficul ty arises from the diverse response times (from 10 -8 to 10- 1 second) of the coupled equations of the system. In this paper a transformation of the dif fusion equations is developed which permits coupling them to mechanical and thermodynamic equations of much slower response times, thus eliminating the difficulties previously encountered in simulating these coupled sets of equations. In the transformation, time is the continuous vari able and energy and space are made discrete. The reactor core is divided into concentric cylindrical regions and the energy is divided into bands. The transformtion involves using natural logarithm of the neutron flux in the center region as a refer ence and determining the change in the ratio of the natural logarithm of the neutron fluxes in the other regions to that in the center region as a result of a regional variation in neutron produc tion. The transformation permits a simulation to cover many decades of continuous change in neutron flux. It also gives directly the deviation from the steady-state neutron flux distribution.