[en] The properties of the variational nodal method for neutron transport calculations are investigated. The method is generalized for three-dimensional multigroup criticality problems in both hexagonal-z and Cartesian geometries. The method is implemented as part of the Argonne National Laboratory Code DIF3D, and applied to a series of benchmark reactor calculations. Variational nodal methods are compared of nodal transport methods based on both interface-current and discrete ordinate approximations. Model problems are used to examine the effect of running each of the three classes of nodal transport methods on computers with massively parallel architectures

[en] The contents of the book are presented under the following chapter headings: (1) nuclear power reactor characteristics, (2) safety assessment, (3) reactor kinetics, (4) reactivity feedback effects, (5) reactivity-induced accidents, (6) fuel element behavior, (7) coolant transients, (8) loss-of-coolant accidents, (9) accident containment, and (10) releases of radioactive materials

[en] Variational nodal transport methods are generalized for the treatment of multigroup criticality problems. The generation of variational response matrices is streamlined and automated through the use of symbolic manipulation. A new red-black partitioned matrix algorithm for the solution of the within-group equations is formulated and shown to be at once both a regular matrix splitting and a synthetic acceleration method. The methods are implemented in X- Y geometry as a module of the Argonne National Laboratory code DIF3D. For few group problems highly accurate P₃ eigenvalues are obtained with computing times comparable to those of an existing interface-current nodal transport method

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[en] A discrete ordinate response matrix method is formulated for the solution of neutron transport problems on massively parallel computers. The response matrix formulation eliminates iteration on the scattering source. The nodal matrices which result from the diamond-differenced equations are utilized in a factored form which minimizes memory requirements and significantly reduces the required number of algorithm utilizes massive parallelism by assigning each spatial node to a processor. The algorithm is accelerated effectively by a synthetic method in which the low-order diffusion equations are also solved by massively parallel red/black iterations. The method has been implemented on a 16k Connection Machine-2, and S₈ and S₁₆ solutions have been obtained for fixed-source benchmark problems in X--Y geometry

[en] This books presents a balanced overview of the major methods currently available for obtaining numerical solutions in neutron and gamma ray transport. It focuses on methods particularly suited to the complex problems encountered in the analysis of reactors, fusion devices, radiation shielding, and other nuclear systems. Derivations are given for each of the methods showing how the transport equation is reduced to sets of algebraic equations suitable for solution on a digital computer. The limitations of the methods and their suitability for different classes of problems are discussed in terms of computer memory, time requirements, and accuracy

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[en] The within-group even-parity neutron transport equation is formulated with complex angular and spatial trial functions and with a complex buckling approximation. Three angular trial functions are compared; finite elements, discrete ordinates, and complex spherical harmonics. When discrete ordinates or finite element basis functions are applied, the differential equations for the real and imaginary parts of the even-parity flux are coupled by the buckling vector. The spherical harmonics equations for the real and imaginary parts of the even-parity flux, however, uncouple when one particular transverse buckling direction is chosen for a two-dimensional problem. Bilinear rectangular finite elements are applied to the spatial variable, the buckled spherical harmonics angular treatment is generalized to arbitrary order, and the resulting formulation is incorporated into a multigroup formalism using a lumped source approximation. The finite element/buckled spherical harmonics multigroup neutron transport code, FESH, has been developed from these approximations, and treats either fixed source problems or criticality eigenvalue problems. The applicability of this method to problems with several thousand spatial nodes has been demonstrated by comparison of numerical results with another spherical harmonics code and with other computational methods. Buckled two-dimensional eigenvalue calculations reveal substantial improvements over the DB² buckling method when transverse transport effects are important

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