Discrete Ordinates Deep Penetration Calculation Method With The Slice Balance Spatial Schemes

The discrete ordinates method,as a classic deterministic transport method,is widely used in the shielding calculation for nuclear installations.As the geometric structure and design proposals become more complex,it is necessary to describe the physical model more accurately.The extremely large amount of calculation for deep penetration problems is a serious challenge for computing resources and simulation efficiency.At the same time,the effects of strong spatial heterogeneity and strong angular anisotropy cannot be ignored for deep penetration problems.The heterogenous distribution of material medium causes the angular flux to become unsmooth or even discontinuous in space.The increase in the penetration distance causes the angular flux and scattering source term to become more anisotropic in angle.The discretization errors of the transport calculation directly affect the computational accuracy of shielding analyses.For the coupling effects of deep penetration,spatial heterogeneity and angular anisotropy in complex shielding problems,this dissertation studies the highly accurate discretization schemes,highly efficient solving algorithm and optimized method to calculate strong anisotropic scattering source,which can improve the reliability of the shielding simulation.The linear short characteristic,exponential short characteristic and slice balance difference-liked schemes are studied,which are capable of suppressing the non-physical spatial oscillations.A new discretization scheme is reconstructed for the linear characteristic method based on the parametric model.The volume moment integral method is proposed to solve the problem of numerical instability for the cavity medium.The response matrix method is used to reduce the expensive cost caused by the multiple integral of exponential terms,and it realizes the flexible reduction of spatial distribution function.The coupling algorithm of the step,linear and exponential short characteristic schemes is explored using the physics-based source dominating factor and spatial shape factor as the estimators to guide the selection of spatial discretization methods.Facing large-scale and complex geometric problems,a multilevel octree grid algorithm is studied for the three-dimensional structured grids,which automatically merges the initial fine meshes according to the mesh material and source strength,and generates a nested multilevel mesh distribution with hanging nodes.It can accurately describe local features and greatly reduces the total number of meshes and computing memory requirements.A recursive transport sweep algorithm is used with the logical search and standard sweep.Multiple mapping methods are proposed for passing boundary angular flux between non-matching grids.An adaptive predictor-corrector mapping algorithm is constructed for the zero-order discretization methods to perform the coarse-to-fine mapping,which improves the mapping accuracy for the optically thick meshes with strong flux attenuation.The fine-to-coarse mapping scheme is optimized for the first-order linear discretization to avoid the generation of negative mapping distributions.The researches on the mapping methods lay the foundation for the accuracy of the multilevel grid calculation.One hybrid method of adjusting scattering cross sections is proposed based on the maximum entropy method and the least square method to generate the non-negative scattering functions with high angular description accuracy,which can improve the accuracy of anisotropic scattering source terms.The transport simulation and numerical analyses are performed for the deep penetration problems.The slice balance spatial discretization schemes have significantly higher accuracy than the finite difference methods for the problems with continuous and discontinuous flux distributions.The optimized linear short characteristic scheme has the advantages of numerical stability and computational efficiency,and the reduced-order step characteristic scheme using the matrix form is faster than the diamond difference method.The linear characteristic scheme needs to control the mesh size within two times the mean free path for the strong flux attenuation problems.For self-designed problems and complex engineering problems with irregular geometry,the multilevel grid algorithm reduces the total number of grids,memory requirements and calculation time by about an order of magnitude under the same modeling accuracy,and the relative error of the local response is controlled within 10%.This algorithm improves the description accuracy of the physical model and the simulation efficiency of shielding calculation.The scattering cross section coupling adjustment algorithm can construct a more accurate non-negative scattering function from the low-order Legendre expansion.The deep penetration simulation of light water shows that the coupling adjustment algorithm controls the relative errors within 2%while the original P3 order expansion has the relative errors of about 8%.The calculation accuracy of scattering sources and flux distributions is improved for the strong anisotropic problems.The research of this subject improves the discrete ordinates shielding calculation method and overcomes the deficiencies of the current algorithms for the deep penetration calculation of complex geometries.The research has the value of further application in large-scale shielding problems.