Computational Methods For Neutron Transport Equation In One-Dimensional Spherical Geometry

In this thesis, we focus on designing efficient computational methods for one-dimensional spherical geometric transport equations based on discrete ordinate method for the practical appli-cation problems. We study the precision and efficiency for numerical methods of neutron transport equations and apply these numerical methods for applied field.For the precision of discrete methods, we construct and analyze finite volume schemes and linear discontinuous finite element method for time-dependent multi-group transport equations. The oscillation occurs in numerical solution for the derivative of flux with respect to time for the exponential scheme and diamond difference scheme of finite volume methods. The linear discontinuous finite element method is generally more accurate than the exponential method and the diamond difference method on coarse meshes. Moreover the differential curve with respect to time variable given by linear discontinuous finite element method retains good smoothness. We construct modified time discrete scheme and second-order time evolution scheme with adaptive time step.For acceleration methods, we present two methods for solving time-dependent transport equa-tions. First, we construct four choices of iterative initial values to solve transport equations. one of which is based on extrapolation of physical process and gives the best result for acceleration. Then, a spatial domain decomposition method is adopted in the computational domain, in which different interface prediction and correction methods are introduced for incident flux on inner in-terface to overcome the difficulty that the conventional sweep method has no spatial parallel degree for one-dimensional spherical transport problems.Moreover, different kinds of particle are classified, and the classified particle transport equa-tions are solved based on decomposition for the requirement in the research of nuclear reaction systems. Last, we analyze and improve the solution methods of eigenvalues for steady state trans-port equation. Some numerical results are presented to demonstrate the accuracy and acceleration effect of the numerical methods proposed.