Positivity-preserving Acceleration Algorithm For Neutron Transport Equation

We study some efficient methods for solving a steady-state,one-group,isotropically-scattering,fixedsource neutron transport problem in planar geometry,and construct an iterative scheme for the coarse mesh rebalance(CMR)method with positivity-preserving acceleration,and carry out a Fourier analysis of the constructed scheme.By solving the spectral radius,it is proved that this method is a good fast convergence.It is proved theoretically that this scheme is a good solution method,and the angular flux and scalar flux obtained can be guaranteed to be nonnegative.In Chapter 1,the physical background of the neutron transport equation and the research status at home and abroad are introduced,and the corresponding solutions are introduced.The difficulties in solving neutron transport equations and the importance of constructing an iterative solution equation with positivitypreserving acceleration is explained.In Chapter 2,a positivity-preserving acceleration iterative method is proposed to solve the neutron transport equation.This method is a method to solve the diagonally dominant matrix of discrete ordinates neutron transport equation by properly defining the rebalance factor of coarse mesh rebalance method.We make the inversion of this matrix nonnegative,and we can obtain the nonnegative rebalance factors,which is crucial for the positive-preserving acceleration methods.In Chapter 3,we do Fourier analysis of some common methods for solving neutron transport equation and Fourier analysis of the constructed positivity-preserving acceleration scheme.Then,we solve the iterative scheme of the spectral radius expression and plot the corresponding graph.