Nuclear reactor kinetics based on hierarchical nodal analysis

The analysis of nuclear reactor power transients requires a considerable amount of computational resources. The main objective of the present thesis is to establish a new solution algorithm called hierarchical nodal kinetics whose main objective is to reduce the computing costs of the time-dependent calculations without introducing unacceptable inaccuracies in the solution. The basis of the method is the definition of one or more intermediate coarser grids over which the reactor problem is solved at a much lower computational cost. To preserve the accuracy of the coarse calculations, the projection of the reactor problem from the finer grids to the coarser meshes is carried out using generalized equivalence theory and so-called discontinuity factors. Two formalisms of hierarchical nodal kinetics are established, time hierarchy and space hierarchy approaches. In the time hierarchy formalism, the solution of the reactor over the coarse grids is treated as the reactor solution (or a part of the reactor solution) for the next time step. In the space hierarchy formalism, the intermediate coarse solutions are used to accelerate the convergence rate of the fine grid problem.;Numerous simulations for both static and dynamic calculations are designed and performed to better understand different aspects of using generalized equivalence theory and thus to correctly evaluate the performance of the hierarchical nodal kinetics method. All test cases are performed for a relatively realistic model of a CANDU-6 reactor. The results obtained from the use of the time-hierarchy formalism resulted in a performance increase of at least 85% compared to the reference solution while maintaining accuracy of the solution. Furthermore, it is demonstrated that by using the space-hierarchy approach, which is a multigrid method, the number of iterations necessary for a given convergence criterion can be reduced by least 50% resulting in a considerable saving in total CPU time.