Finite Element Solutions of Space-Time Nonlinear Reactor Dynamics

The finite element method was used to solve a nonlinear two-dimensional reactor dynamics equation. The system considered is a superprompt critical fast reactor, subjected to the prompt feedback condition. Various nonuniform initial disturbances allow the examination of the spatial dependence of neutron dynamics. Under exact numerical treatment, the quadratic nonlinearity in the dynamics equation transforms into an N × N² matrix operator, where N is the system degree of freedom. This large matrix size taxes heavily on computer time and storage. The results obtained here can be considered as a numerical standard. It is found that there is a strong spatial dependence during the early phase of the transient, and that this dependence increases with increasing discontinuity in initial conditions. The transient behavior at each point in space also depends strongly on the spatial distribution and magnitude of the initial disturbances.