Neural Network Based Deep Learning Method for Multi-Dimensional Neutron Diffusion Problems with Novel Treatment to Boundary

In this paper, the artificial neural networks (ANN) based deep learning (DL) techniques were developed to solve the neutron diffusion problems for the continuous neutron flux distribution without domain discretization in advance. Due to its mesh-free property, the DL solution can easily be extended to complicated geometries. Two specific realizations of DL methods with different boundary treatments are developed and compared for accuracy and efficiency, including the boundary independent method (BIM) and boundary dependent method (BDM). The performance comparison on analytic benchmark indicates BDM being the preferred DL method. Novel constructions of trial function are proposed to generalize the application of BDM. For a more in-depth understanding of the BDM on diffusion problems, the influence of important hyper-parameters is further investigated. Numerical results indicate that the accuracy of BDM can reach hundreds of times higher than that of BIM on diffusion problems. This work can provide a new perspective for applying the DL method to nuclear reactor calculations.

Higher order TN approximation for the neutron diffusion problem in a slab reactor

Higher order approximations of the Chebyshev polynomials of first kind (TN) are used for the first time in calculation of the diffusion lengths of monoenergetic neutrons in a homogeneous slab. In the method, the diffusion lengths of the neutrons are calculated using various values of the c, the number of secondary neutrons per collision. First, the traditional Legendre polynomials (PN) approximation and then the present TN method are used separately. The numerical results for the diffusion lengths are tabulated in the tables up to an order of N = 9. A brief comparison is also done between the results obtained from the present method and the ones in literature. The advantages of the present method can easily be observed from the good accordance between results given in the tables for comparison and its easily executable equations. For many of the c values, the results obtained from TN method are better than the results obtained from PN method.

Simulation of transients in ads reactors in three-dimensional geometry

Accelerator-Driven System, ADS, belong to the new generation of advanced reactors being developed that promise to drastically reduce the life of radioactive waste by, for example, the transmutation process. Subcritical reactor designs of the ADS type have attracted worldwide attention and are the subject of research and development in several countries. The purpose of this work is to simulate transients associated with ADS. It adopted the neutron diffusion model that leads the spatial kinetics equations. These equations are solved by the known numerical method of finite differences. The simulations are performed considering transients related to the variations in the intensity of the proton flux provided by the particle accelerator acting in a sub-critical reactor in three-dimensional geometry for two energy groups and six groups of delayed neutron precursors.