Deterministic Numerical Methods for Unstructured-Mesh Neutron Transport Calculation (Woodhead Publishing Series in Energy)

Description

Deterministic Numerical Methods for Unstructured-Mesh Neutron Transport Calculation presents the latest deterministic numerical methods for neutron transport equations (NTEs) with complex geometry, which are of great demand in recent years due to the rapid development of advanced nuclear reactor concepts and high-performance computational technologies. This book covers the wellknown methods proposed and used in recent years, not only theoretical modeling but also numerical results. This book provides readers with a very thorough understanding of unstructured neutron transport calculations and enables them to develop their own computational codes. The fundamentals, numerical discretization methods, algorithms, and numerical results are discussed. Researchers and engineers from utilities and research institutes are provided with examples on how to model an advanced nuclear reactor, which they can then apply to their own research projects and lab settings. Front Matter Copyright Contributors Foreword Preface Neutron transport equation Introduction Definition of the ordinates and basic elements Coordinate system Neutron density, angular flux, and current First-order transport equation Derivation of the NTE Different forms of divergence operator Definite conditions Second-order transport equation Second-order even-parity neutron transport equation Second-order SAAF transport equation Integral form of transport equation Brief introduction to the numerical solution to NTE Eigenvalue problem and source iteration method Overview of approximate solution for neutron transport equation The adjoint transport equation Adjoint operator Adjoint neutron transport equation Neutron importance function References Collision probability method Integral-form neutron transport equation Collision probability for solving NTE CPM calculation flowchart Collision probability evaluation Collision probability properties References Transmission probability method for triangular meshes Basic equations Two-dimensional calculation Approximation Probability calculation Leakage probability calculation Transmission probability calculation Boundary conditions and unstructured-mesh sweeping Three-dimensional calculation Approximation Probability calculation Leakage probability calculation Transmission probability calculation Boundary conditions and unstructured-mesh sweeping Numerical results 2D problem 3D problem References Current-coupled collision probability method Theory Introduction Discretization The coupling equations Response matrices Numerical results The problems of regular and irregular cells The 2D C5G7 problem References The method of characteristics Basic equations Two-dimensional MOC Long ray tracing technique Modular ray tracing technique Three-dimensional MOC 3D modular ray tracing technique Angular quadrature sets Geometry pretreatment method 2D/1D fusion method Basic equations Potential negative total sources Traditional leakage splitting method The improved leakage splitting method Numerical results Irregular 2D geometric problem Single fuel particle problem C5G7 problem References PN-FEM method Basic equations First-order transport equation Weak formulation from weighted residual method Discretization of the equation Angular approximation Spatial discretization Boundary conditions Stabilized finite element method SUPG method GLS method TG method SGS method Unified expression of stabilized finite element method Value of stabilization parameter Finite element implementation Evaluation of integrals Angular integrals Spatial integrals Spatial-angular integrals Evaluation of algebraic equation LHS matrix RHS vector Assemble and solve the equations Numerical results 1D Analytical problem 1D Reed cell problem Maynard Watanabe problem Strong scattering problem Strong absorption problem IAEA 5-region fixed source problem Kobayashi problem 3i Helium cooling ceramic breeder for fusion DEMO Typical tritium breeding blanket module of CFETR Chinese fusion engineering test reactor Appendix 1. Recurrence relation of spherical harmonics Appendix 2. Shape function of simplex element References The discrete ordinate method Establishment of basic equations Establishment of one-dimensional discrete ordinate equation Establishment of multidimensional discrete ordinate equation Spatial variable discretization SN finite element method for unstructured geometry Least-squares variation Spatial discretization Treatment of boundary condition Solution of the stiffness matrix Numerical results SN nodal method for triangular prism meshes Spatial discretization Numerical solution process Selection of the quadrature set Numerical results Appendix 1 Appendix 2 Appendix 3 Appendix 4 References Mesh-free method Introduction of mesh-free method Theory of mesh-free method Support domain Formulation Numerical scheme Numerical procedure and core development Numerical results 2D2G problem 2D4G problem 2D-IAEA problem 2D-TWIGL problem 4G-LMFBR problem Natelson problem Transient localized source problem Discussions References Other methods Wavelet expansion method in neutron transport Wavelet basis function Wavelet expansion method Numerical results Heterogeneous variational nodal method The VNM formulations The legacy multigroup Guass-Seidel (MG GS) algorithm The within group red-black Gauss-Seidel (RBGS) algorithm Hybrid method of Monte Carlo and method of characteristics The criticality calculation of transport equation Division of energy ranges The MOC calculations in the fast and thermal energy ranges The Monte Carlo simulation in the resonance energy range The hybrid Monte Carlo deterministic method in energy range Numerical results References Index A B C D E F G H I J K L M N O P Q R S T U V W X