Global nonlinear analysis code for nuclear systems

This work incorporates into a computer code a recently developed formalism for globally computing the critical parameters of nonlinear problems: bifurcations, limit points, and extrema (maxima and minima). The local sensitivities (i.e., first-order derivatives) of the system's state variables (e.g., fluxes, power, temperatures) at any point in the system's phase space are also determined. After initially testing the code with a simple unconstrained nonlinear optimization problem, the code was expanded to handle more sophisticated systems with active or inactive constraints.

There are two test problems used to verify the code's capabilities. One is an unconstrained nonlinear BWR model consisting of a system of five nonlinear equations. This problem was chosen in order to verify the code's ability to locate the first-order bifurcations of this BWR model. The second test problem is a simple constrained optimization problem that is used to test the inactive/active constraint option implemented into the code. The results obtained from these test problems reveal that the code can accomodate active or inactive constrained optimization problems accurately and efficiently.