Reactor Core Physics Simulation Research Based On The Finite Difference Method

The accuracy of nuclear reactor physics calculations is important to design nuclear reactor and for simulating and Verifying security. In recent years, It is a hot topic how more accurate calculation of the reactor core distribution and variations in time and space.Solving the three-dimensional neutron diffusion equation needs discrete both in space and time. In space discrete terms, finite difference method has a good mathematical basis, with second-order accuracy. Finite difference method is not only better than the nodal method in terms of the accuracy of calculation, but also the total amount of the calculation is less than the calculation method of neutron transport equation. In terms of discrete time, implicit difference method, ? method and time integration method are used for solving the multi-dimensional transient diffusion equation. Because of stiff problem, it cannot be used to solve the problem in large time steps. Exponential transformation method can slow the rate of change of neutron flux, making the transformed equation to become easier to solve, and to reduce error. The equation can use several methods previously described to be solved, which is used the exponential transformation method.Based on finite difference program CITATION code, three-dimensional steady-state computing program is written. Using prompt jump approximation, implicit difference method,? method, time integration method based on exponential transform method, The three-dimensional space-time neutron kinetics transient solver is written based on the finite difference steady state computer program. Prompt jump approximation, implicit difference method and the ? method are using line over relaxation solver, which is used in steady state calculations, solving linear equations. Based exponential transformation time integration method, in order to speed up the computation, Krylov subspace methods related solver is written. Which uses a conjugate gradient squared method (CGS) solver has been very good results. In order to use CGS solver, compact storage of the coefficient matrix is used, and the compressed storage-related matrices and vectors calculation routine is prepared.By verifying the benchmark problems, the preparation of three-dimensional steady-state calculation program and line over-relaxation solver used in the calculation the steady state results are accurate. In the transient calculation, prompt jump approximation, the implicit difference method, 0 method, based on exponential transformation time integration method is used to solve the LMW benchmark problem. The results of these methods, the numbers of iterations, and the computation time have been compared. Based on the results exponential transformation time integration method is slightly better than the other three algorithms on calculation results.