Thesis Open Access

A neutron noise solver based on a discrete ordinates method.

Huaiqian YI

Thesis supervisor(s)

Paolo Vinai

A neutron noise transport modelling tool is presented in this thesis. The simulator allows to
determine the static solution of a critical system and the neutron noise induced by a prescribed
perturbation of the critical system. The simulator is based on the neutron balance equations in
the frequency domain and for two-dimensional systems. The discrete ordinates method is used
for the angular discretization and the diamond finite difference method for the treatment of the
spatial variable. The energy dependence is modelled with two neutron energy groups. The
conventional inner-outer iterative scheme is employed for solving the discretized neutron
transport equations. For the acceleration of the iterative scheme, the diffusion synthetic
acceleration is implemented.
The convergence rate of the accelerated and unaccelerated versions of the simulator is studied
for the case of a perturbed infinite homogeneous system. The theoretical behavior predicted by
the Fourier convergence analysis agrees well with the numerical performance of the simulator.
The diffusion synthetic acceleration decreases significantly the number of numerical iterations,
but its convergence rate is still slow, especially for perturbations at low frequencies.
The simulator is further tested on neutron noise problems in more realistic, heterogeneous
systems and compared with the diffusion-based solver. The diffusion synthetic acceleration
leads to a reduction of the computational burden by a factor of 20. In addition, the simulator
shows results that are consistent with the diffusion-based approximation. However,
discrepancies are found because of the local effects of the neutron noise source and the strong
variations of material properties in the system, which are expected to be better reproduced by a
higher-order transport method such as the one used in the new solver.

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