The Mean Projection Method Of A Kind Of Unsteady Neutron Transport Equation

The transport equation is a kind of mathematical model to study the macro-scopic transport phenomenon of the system,which can be expressed as a differential integral equation,and is widely used in many fields such as physics,engineering,quantum chemistry and so on.The eigenvalue problem of transport equations has always been a kind of important research topic,and the numerical solutions of eigenvalues and eigenvectors have also attracted the attention of many researchersThis paper mainly studies a class of one-dimensional planar geometric neutron transport equation with fixed boundary conditions,and it is a kind of steady and non-stationary transport equation where reflection and fission are isotropic.For this equation,this paper will also studies its eigenvalue related issues and considers the mean projection method for discretization in Lp(1<p<?)space,so the interval mean is used to replace the interval function to discretize the given velocity variable in the equation.Then,the mean projection operator is defined,and the properties of the operator are verified.the mean projection algorithm for discretization of the neutron transport equation is given,and it is used to analyze the convergence of eigenvalues and eigenvectors.Finally,the convergence of the approximate eigen-values and eigenvectors is proved theoretically,and the higher convergence speed is obtained,which further verifies the rationality of the mean projection methodCompared with the existing multi-group approximation theory and the discrete ordinate method,the results obtained have higher convergence order,and the con-vergence speed of eigenvalues and eigenvectors is faster.In practical application,this will greatly reduce the workload of calculation,reduce the error rate,and get a result closer to the analytical solution.Moreover,it is not only of great help to the calculation of the original transport equation,but also provides ideas for the study of other types of transport equations.At the same time,it is also of great significance to the future study of the transport equation and its theory.