Monte Carlo Particle Transport Variance Reduction Method

Radiation shielding analysis is one of the most important part of current nuclear safety assessment.Accurate radiation shielding calculation is the most important part of nuclear energy system design and operation.Compared with deterministic method,Monte Carlo method is the first choice for radiation shielding analysis in current situation.MC method analyzes a large number of neutron behavior by random simulation,and obtains a statistical mean estimate.It has the characteristics of accurate description of geometric model and complex source,continuous cross section and high robustness,and it is becoming widely used in shielding analysis.The small probability deep-penetration problem is the key of MC shielding calculation and the key problem to be solved urgently.When the system is less than 10 mean free path,MC method can get the exact result.When the system is larger than a dozen or 100 times the mean free path,the result of MC method is not reliable,or even the computation result can not be obtained.However,increasing the samples would increase the calculation time exponentially.Variance reduction method can guide particles transport to the target area.Therefore,effective variance reduction methods are needed to solve the deep-penetration problem.But traditional variance reduction methods can not meet the development of current nuclear energy system.Faced with the local problem and global problem,based on neutron transport theory,adjoint transport theory and zero variance theory,we proposed several variance reduction methods for huge shielding block problem and huge source problem.First introduced the anti-forward variance reduction method,the detector position and source area in forward calculation is set as source and tally area in anti-forward calculation respectively.Thus the anti-forward model has been constructed.The source bias parameters and transport bias parameters are constructed by using the anti-forward flux,and particles and computing resources are converged to the detectors.This method increases the statistics of detection region and reduces the statistical error.This method does not need to consider the program coupling problem and mesh matching,which greatly improves the Monte Carlo deep-penetration shielding calculation efficiency.Secondly,faced with huge shielding block problem,we put forward transport bias parameter and source bias parameter generation method for space problem and spatial-energy problem respectively.The particles and computing resources are uniformly guided from near source region to the whole model.Aiming at the empty mesh problem which affects the computation efficiency,pseudo flux method based on point flux algorithm has been proposed,which estimates the uncounted flux roughly,and the computation efficiency has been greatly improved.The method only needs to establish a Monte Carlo model,without considering the twice modeling and mesh matching,and has a certain engineering practicality.Then,we introduce the process of MC multi-group adjoint computation,and the method of constructing adjoint transport model through the forward transport model,and the importance function generation method based on MC multi-group calculation.Finally,the local variance method based on the Monte Carlo multi-group adjoint calculation is proposed and implemented.Compared with the local couple method of SN method and MC method,this method can solve the complex geometric model shielding problem.It solves the problem of mesh matching,and avoids the time consuming of the twice modeling.At last,the research of similarity importance based on MC multi-group adjoint calculation is introduced.The method of changing the density of material and moving the location of adjoint source to obtain similar importance is proposed,and the importance function can improve the calculation efficiency greatly.In order to make the multiple detectors converge at the same time,the importance function for multiple detectors is proposed.In order to make the adjoint calculation of each single point as the adjoint source term consistent with the adjoint flux at the source area of the forward calculation,that is,the contribution of the forward source term to each detector is consistent,the adjoint source strength is approximately set as the reciprocal of the forward flux.Finally,we propose the global variance reduction method based on multi-group adjoint calculation,aim at huge source problem,particles and computation resources are biased to each corner of the system.The variance reduction methods proposed in this thesis are validated by the shielding benchmark which issued by OECD-NEA.The results show that variance reduction methods can improve computation efficiency and solve the difficult convergence problem.The objective of constructing a set of effective variance reduction methods for the Monte Carlo deep-penetration shielding calculation has been completed.