Search

This work focuses on the k-eigenvalue problem of the neutron transport equation. The variables of interest are the largest eigenvalue (keff) and the corresponding eigenmode is called the fundamental mode. Mathematically, this problem is usually solved using the power iteration method. However, the convergence of this algorithm can be very slow, especially if the dominance ratio is high as is the case in some reactor physics applications. Thus, the power iteration method has to be accelerated in some ways to improve its convergence. One such acceleration is the Chebyshev acceleration method which has been widely applied to legacy codes. In recent years, nonlinear methods have been applied to solve the k-eigenvalue problem. Nevertheless, they are often compared to the unaccelerated power iteration. Hence, the goal of this paper is to apply the Anderson acceleration to the power iteration, and compare its performance to the Chebyshev acceleration.

Presently, APOLLO3® /MINARET solves the transport equation using the multigroup Sn method with discontinuous finite elements on triangular meshes with Lagrange polynomial bases. The goal of this work is to solve the spatial problem on hexagonal geometries in the context of honeycomb lattice reactors, without further refining the computational mesh. The idea here is to construct high-order basis functions on the hexagonal element in order to improve the trade-off between computational cost and accuracy, in particular for multiphysics simulations where, often, thermalhydraulic modelling requires only assembly-average cross-sections to be defined (e.g. severe accident of fast breeder reactors) i.e. the assemblies are assumed homogeneous. One approach to achieve this goal is through the use of generalised barycentric functions such as the Wachspress rational functions. This research endeavour deals with the application of Wachspress rational functions to the neutron transport equation for hexagonal geometries up to order 3. With this method, it is possible to decrease the number of spatial unknowns required for the same accuracy, and thus the computational burden for complex geometries, such as honeycomb lattices is reduced.

In the context of the simulation of the Severe Accidents (SA) in Light Water Reactors (LWR), we are interested on the in-core corium pool propagation transient in order to evaluate the corium relocation in the vessel lower head. The goal is to characterize the corium and debris flows from the core to accurately evaluate the corium pool propagation transient in the lower head and so the associated risk of vessel failure. In the case of LWR with heavy reflector, to evaluate the corium relocation into the lower head, we have to study the risk associated with focusing effect and the possibility to stabilize laterally the corium in core with a flooded down-comer. It is necessary to characterize the core degradation and the stratification of the corium pool that is formed in core. We assume that the core degradation until the corium pool formation and the corium pool propagation could be modeled separately. In this document, we present a simplified geometrical model (0D model) for the in-core corium propagation transient. A degraded core with a formed corium pool is used as an initial state. This state can be obtained from a simulation computed with an integral code. This model does not use a grid for the core as integral codes do. Geometrical shapes and 0D models are associated with the corium pool and the other components of the degraded core (debris, heavy reflector, core plate…). During the transient, these shapes evolve taking into account the thermal and stratification behavior of the corium pool and the melting of the core surrounding components. Some results corresponding to the corium pool propagation in core transients obtained with this model on a LWR with a heavy reflector are given and compared to grid approach of the integral codes MAAP4.