Wavelet Method Modeling Of Neutron Transport Equation And Optimization Research Of Nodal Expansion Method

Two-step reactor physics calculation is one of the important researches of nuclear reactor engineering simulation,including the detailed neutron transport calculation of heterogeneous assembly or pin,the calculation of cross-section parameters and the coarse-mesh nodal calculation of homogenized reactor cores.It is of great research significance on the reactor physics calculation of two-step method to reduce the calculation error and implementation difficulty of each key step.This paper studies and optimizes the key steps of two-step methods,aiming to effectively reduce the calculation error while maintaining the computational efficiency.The wavelet basis function expansion based on neutron transport model is established for detailed simulation.The influence of the basis function in the nodal expansion method on the calculation accuracy is studied and an optimization scheme is proposed.A multi-dimensional high-order least-squares method is established for parameterized cross-section calculations,in which all the state parameters are fitted simultaneously without grouping.A detailed neutron transport calculation model by using hexahedral wavelet function is constructed.The wavelet function is used as the basis function to expand the neutron transport angular variable and the finite-differential method is used to deal with the spatial discretization.Based on these techniques,a high-accurate wavelet based on neutron transport（WNT）calculation model is established.Numerical results show that the WNT model established in this paper has high accuracy and has good applicability to typical neutron transport boundary conditions and complex regions.Compared with the traditional discrete-ordinate method,the WNT method can effectively reduce the ray effect and obtain higher accuracy.The high-accurate nodal expansion method（NEM）is studied and developed.Based on the NEM,the partial neutron flux density,leakage term and source term are expanded by using the polynomial function with parameters.The influence of each parameter on calculation accuracy can be analyzed from the numerical results.According to different core structures and material properties of assembly,the undetermined parameters are tested for better results.Compared with the traditional polynomial function of the NEM,it is proved that this method can obtain more accurate effective multiplication factor k_eff and power density distribution.A cross-section parameterization calculation method for multi-parameter fitting without grouping is established.The least-squares model that suits for multi-dimension parameters is constructed in this paper.Compared with the results of grouped coupling fitting,it is proved that this method can effectively reduce the calculation error.In conclusion,in order to more accurately realize the two-step reactor core calculation,a reasonable optimization scheme for each key step is proposed.The suitable model is constructed to verify the correctness and the reliability.This work can provide a new idea for the optimization and improvement of the two-step method.