Study On Source Iteration Acceleration Tor Neutron Transport Equation

In various applications such as nuclear reactor numerical simulation,it is neces-sary to solve the neutron transport equation.The solution of the neutron transport equation occupies the main calculation in many important applications of numeri-cal simulation.The neutron transport equations are used to describe the transport process of the neutron population in the medium.This equation is a kind of par-tial differential integral equations of multidimensional independent variables about space,time,energy and direction.Because of the complexity of the equation,it can only be solved numerically in general.After the neutron transport equation is dis-cretized,a large scale nonlinear equations are obtained.The source iteration is the most popular method for solving the discretized neutron transport equation.Usu-ally,the source iteration converges slowly.By now there has been much research on the acceleration for source iteration.One of widely used acceleration method is the nonlinear diffusion acceleration method(NDA).NDA method can be used to accelerate the solution of fixed-source problem,a typical anisotropic scattering model.However,the effect of NDA method will deteriorate when the scattering source is less isotropic.Anderson acceleration method(AA)has been widely used to improve the convergence rate of fixed point iteration in recent years.Because the source iteration process can be regarded as a kind of fixed point iteration,AA method can be used naturally to improve the convergence rate of source iteration.In this paper,the comparison study is conducted about the effectiveness of NDA method and AA method,and analysis about the applicability of the methods is given.Furthermore,by the combination of the methods,two kinds of new methods,AA-NDA,AA-NDA(2)is obtained.The combination method of AA and NDA can be used to remedy the degraded performance of NDA when scattering is anisotrop-ic.Through numerical examples in one-dimensional case,the different acceleration effect of AA method,NDA method,AA-NDA,AA-NDA(2)method are compared for solving the neutron transport equation of fixed source.In addition,in the case of three-dimensional unstructured grid parallel computing,The results of AA accel-erated source iteration method and non-AA accelerated source iteration method are compared.