Symmetry Study Of Two-dimensional Neutron Transport Equation

Since the discovery of neutrons by British scientist Chadwick in 1932 , the neutron transport theory has been developing rapidly with the emergence of nuclear reactors and nuclear weapons. The neutron transport equation is too complex to be solved analytically. By the joint efforts of mathematicians and physicists, there are a series of numerical methods and applied codes to solve the equation.This paper focuses on the 1-D spherically symmetrical problem in the research of the 2-D neutron transport equation, which include mainly two items as follows:1. In 2-D spherical geometry, by means of the finite volume method and the dedicated constraint grid method, the 2DSK1DS scheme of nonnegativity and conservation is constructed, and it is proved theoretically that the scheme can keep 1-D spherical symmetry. The numerical results validate the 1-D spherical symmetry of the scheme.2. In 2-D cylindrical geometry, it has been proven to be inappropriate that the traditional equation is used to study the 1-D spherical symmetry. In view of this, combining the variables(x, r) of 2-D cylindrical geometry space with the variables (μ,β) of the 2-D spherical phasespace, the transport equation of new form is inducted. Aim at the equation, by means of the finite volume method and the dedicated constraint grid method, the 2DCK1DS scheme of nonnegativity and conservation is constructed, and it is proved theoretically that the scheme can keep 1-D spherical symmetry. In the aspect of numerical computing, the 1-D spherical symmetry of the scheme is validated by the calculation for the 1-D spherical symmetry models, and it is explained by the calculation for the 2-D spherical symmetry models that the scheme has the numerical results which are almost identical with those coming from the current 2-D scheme.