Multi-Level Adaptive Source Iteration Acceleration Method

Neutron transport equation is simplified into linear equations or matrix eigenvalue problems after discreted by the discrete ordinates method(SN),which are mostly solved by iteration method.Source iteration method(SI)becomes the most classical method for solving neutron transport equation after discreted because of its clear physical interpretation and strict convergence analysis.At the same time,SI also has some corresponding disadvantages:when solving neutron transport problems with large optical thickness and high scattering ratio,the convergence speed is slow and the calculation takes long time.Since SN directly discretizes multi-dimensional independent variables such as energy,space and angle in transport equation,a large amount of calculation and data storage space are required,and the cost of calculation time is large.Therefore,research on the source iteration acceleration methods is necessary.In this paper,partial current rebalance acceleration method(PCR)and angle multigrid acceleration method(AMG)are the main research contents,and the theoretical formula derivation and programming implementation are carried out.The stability analysis of PCR is carried out by the Fourier method,and the acceleration effect test of two methods are analyzed by examples.The sensitivity of the two key parameters of PCR acceleration method,the rebalance factor convergence criterion EPS-F and the maximum iteration number MaxIter-F,are tested and analyzed.Comparative analysis of the acceleration characteristics of PCR and AMG is completed.Based on the different acceleration characteristics of two acceleration methods,couple the two methods into PCR&AMG coupling acceleration method and program,implementing multi-level adaptive source iteration acceleration method.Then test and analyze the acceleration effects of PCR&AMG coupling acceleration method through examples.The test results show that PCR method can effectively accelerate SI.In the multi-group transport problem,the acceleration effect on the thermal neutron zone is particularly obvious,the ratio of iteration number can be 4 to 17 times.EPS-F and MaxIter-F can affect PCR acceleration by affecting the accuracy of the PCR factor FI,J,k.When the value of EPS-F is small(1×10-3)and Maxlter-F is moderate(30?50),PCR has good stability and ideal acceleration effect.Compared PCR with AMG,we find that AMG has better acceleration stability than PCR;PCR is better than AMG in the early iteration of SI,and then the acceleration effect is gradually attenuated until disappearing.AMG provides lasting and effective acceleration throughout the solution.The test results of PCR&AMG coupling acceleration method show that PCR&AMG coupling method has better acceleration effect than PCR or AMG,implementing multi-level adaptive source iteration acceleration method.PCR&AMG coupling acceleration method provides more stable and more efficient acceleration for SI,effectively improving the efficiency of shielding calculations.