université de montréal développement de la méthode des ...

viii
ABSTRACT
This project is dedicated to the implementation of the method of characteristics
for lattice calculations in the neutronics modeling of nuclear reactors. A lattice
calculation is a sequence of models that require the solution of the neutron transport
equation at different stages. Within this framework, the collision probability
method has been the dedicated tool for a long time. Nowadays, for the multigroup
flux calculation, the method of characteristics tends to supplant collision probability
approaches thanks to its practical capability of treating configurations with a
large number of regions and anisotropic scattering. However, for the other stages
of a lattice calculation, the collision probability method remains the only solver
used. In this work, beyond the computational development related to the method
of characteristics in itself, the main idea is to extend the usage of this method to
all the calculation stages that involve the solution of the transport equation.
In this context, the method of characteristics was implemented for 2D geometries
with exact and approximated boundary conditions. Special care was taken for
the development of acceleration techniques adapted to the different contexts. This
acceleration strategy is based on two general classes of methods, synthetic preconditioning
techniques and Krylov iterative methods, by analogy with the resolution
of large linear systems. An already existing preconditioner was selected ; the work
has consisted in detailing the fundamental assumption of this method, performing a
performances analysis prior and posterior to its implementation and, starting from
there, improving it. A Krylov method was chosen and its implementation with the
previous preconditioner in the special context of the characteristic method has been
carried out. Besides, for comparison purpose, another preconditioning technique
and another Krylov method were implemented.
Apart from these computational developments, some related investigations were
carried out in order to clarify some theoretical and practical aspects related to the