Download or read book A Quadratic linear Nodal Discrete Ordinates Method for Neutron Transport in X Y Geometry written by Tim D. Bohm and published by . This book was released on 1996 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Analytical Nodal Discrete Ordinates Solution to the Transport Equation in Cartesian Geometry written by Joshua Rocheleau and published by . This book was released on 2020 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: A novel Analytical Nodal Discrete Ordinates (ANDO) method for the solution of the discrete ordinates (SN) neutron transport equation in cartesian geometry is presented. A nodal method approximates the multi-dimensional transport equation as a system of coupled one-dimensional transport equations along each coordinate axis by transverse integration. The resulting transverse-integrated equations can then be discretized. The discretization utilized in the ANDO method is based on a recent closed-form analytical solution in slab geometry to give a truly closed-form solution on the computational cell. Further, the closed-form solution on any 2n heterogenous domain is also readily obtained. The new ANDO method is free from spatial truncation error within the computational cell and is limited in accuracy only by the approximation used for the transverse leakage, as are all analytical nodal methods. Results for constant, linear, and quadratic transverse leakage approximations are presented. The ANDO method possesses a number of favorable properties such as high accuracy, rapid convergence, asymptotic preserving, positivity preserving, near linear computational complexity, and is local-hp adaptive. It is also shown that the ANDO method can easily be extended to higher order transverse leakage approximations, to 3-dimensional cartesian geometry, and to multi-group.
Download or read book Nodal Methods for Discrete ordinates Transport Problems in x Y Geometry written by and published by . This book was released on 1981 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A nodal method has been developed for improved spatial differencing of the discrete-ordinates form of the x, y geometry transport equation. In applying this method, spatial flux expansions are assumed along the edges of each solution node (mesh cell), and flux and source expansions are assumed in the interior of the node. Nodal method schemes are thus identified by the expansions used for node edges and node interior. Nodal schemes assuming constant-constant, constant-linear, and four forms of linear-linear expansion have been developed, programed, and used in the analysis of eigenvalue (k/sub eff/) and shielding problems. Nodal results are compared with those obtained by means of the diamond-difference scheme. On the basis of results of eigenvalue test problems examined by the authors, it appears that the linear-linear nodal method schemes are more cost effective than the diamond-difference scheme for eigenvalue (k/sub eff/) problems. These nodal schemes, although more computationally costly than the diamond scheme per mesh cell, yield results of comparable accuracy to those from diamond with far fewer mesh cells. A net savings in both computer time and storage is obtained with the nodal schemes when compared with the diamond scheme for the same accuracy of results. For shielding problems both the constant-linear and linear-linear nodal schemes are superior to the diamond scheme in the sense of reduced computer time and storage for the same accuracy in results. 2 figures, 2 tables.
Download or read book A Linear Characteristic nodal Transport Method for the Two dimensional x Y geometry Multigroup Discrete Ordinates Equations Over an Arbitrary Triangle Mesh written by Richard R. Paternoster and published by . This book was released on 1983 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Computational Methods of Neutron Transport written by Elmer Eugene Lewis and published by Wiley-Interscience. This book was released on 1984 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Discrete Ordinates Approximation to the Neutron Transport Equation Applied to Generalized Geometries written by Mark David DeHart and published by . This book was released on 1992 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Solution of Transient and Steady state Neutron Transport Problems written by Bengt G. Carlson and published by . This book was released on 1959 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Intercomparison of the Finite Difference and Nodal Discrete Ordinates and Surface Flux Transport Methods for a LWR Pool reactor Benchmark Problem in X Y Geometry written by and published by . This book was released on 1983 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the present work is to compare and discuss the three of the most advanced two dimensional transport methods, the finite difference and nodal discrete ordinates and surface flux method, incorporated into the transport codes TWODANT, TWOTRAN-NODAL, MULTIMEDIUM and SURCU. For intercomparison the eigenvalue and the neutron flux distribution are calculated using these codes in the LWR pool reactor benchmark problem. Additionally the results are compared with some results obtained by French collision probability transport codes MARSYAS and TRIDENT. Because the transport solution of this benchmark problem is close to its diffusion solution some results obtained by the finite element diffusion code FINELM and the finite difference diffusion code DIFF-2D are included.
Download or read book New Splitting Iterative Methods for Solving Multidimensional Neutron Transport Equations written by Jacques Tagoudjeu and published by Universal-Publishers. This book was released on 2011-04 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis focuses on iterative methods for the treatment of the steady state neutron transport equation in slab geometry, bounded convex domain of Rn (n = 2,3) and in 1-D spherical geometry. We introduce a generic Alternate Direction Implicit (ADI)-like iterative method based on positive definite and m-accretive splitting (PAS) for linear operator equations with operators admitting such splitting. This method converges unconditionally and its SOR acceleration yields convergence results similar to those obtained in presence of finite dimensional systems with matrices possessing the Young property A. The proposed methods are illustrated by a numerical example in which an integro-differential problem of transport theory is considered. In the particular case where the positive definite part of the linear equation operator is self-adjoint, an upper bound for the contraction factor of the iterative method, which depends solely on the spectrum of the self-adjoint part is derived. As such, this method has been successfully applied to the neutron transport equation in slab and 2-D cartesian geometry and in 1-D spherical geometry. The self-adjoint and m-accretive splitting leads to a fixed point problem where the operator is a 2 by 2 matrix of operators. An infinite dimensional adaptation of minimal residual and preconditioned minimal residual algorithms using Gauss-Seidel, symmetric Gauss-Seidel and polynomial preconditioning are then applied to solve the matrix operator equation. Theoretical analysis shows that the methods converge unconditionally and upper bounds of the rate of residual decreasing which depend solely on the spectrum of the self-adjoint part of the operator are derived. The convergence of theses solvers is illustrated numerically on a sample neutron transport problem in 2-D geometry. Various test cases, including pure scattering and optically thick domains are considered.
Download or read book A Discrete Ordinates Approximation to the Neutron Transport Equation Applied to Generalized Geometries written by and published by . This book was released on 1992 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: A method for applying the discrete ordinates method for solution of the neutron transport equation in arbitary two-dimensional meshes has been developed. The finite difference approach normally used to approximate spatial derivatives in extrapolating angular fluxes across a cell is replaced by direct solution of the characteristic form of the transport equation for each discrete direction. Thus, computational cells are not restricted to the traditional shape of a mesh element within a given coordinate system. However, in terms of the treatment of energy and angular dependencies, this method resembles traditional discrete ordinates techniques. Using the method developed here, a general two-dimensional space can be approximated by an irregular mesh comprised of arbitrary polygons. The present work makes no assumptions about the orientations or the number of sides in a given cell, and computes all geometric relationships between each set of sides in each cell for each discrete direction. A set of non-reentrant polygons can therefore be used to represent any given two dimensional space. Results for a number of test problems have been compared to solutions obtained from traditional methods, with good agreement. Comparisons include benchmarks against analytical results for problems with simple geometry, as well numerical results obtained from traditional discrete ordinates methods by applying the ANISN and TWOTRAN computer programs. Numerical results were obtained for problems ranging from simple one-dimensional geometry to complicated multidimensional configurations. These results have demonstrated the ability of the developed method to closely approximate complex geometrical configurations and to obtain accurate results for problems that are extremely difficult to model using traditional methods.
Download or read book TRIDENT written by and published by . This book was released on 1977 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: TRIDENT solves the two-dimensional-multigroup-transport equations in rectangular (x-y) and cylindrical (r-z) geometries using a regular triangular mesh. Regular and adjoint, inhomogeneous and homogeneous (k/sub eff/ and eigenvalue searches) problems subject to vacuum, reflective, white, or source boundary conditions are solved. General anisotropic scattering is allowed and anisotropic-distributed sources are permitted. The discrete-ordinates approximation is used for the neutron directional variables. An option is included to append a fictitious source to the discrete-ordinates equations that is defined such that spherical-harmonics solutions (in x-y geometry) or spherical-harmonics-like solutions (in r-z geometry) are obtained. A spatial-finite-element method is used in which the angular flux is expressed as a linear polynomial in each triangle that is discontinous at triangle boundaries. Unusual Features of the program: Provision is made for creation of standard interface output files for S/sub N/ constants, angle-integrated (scalar) fluxes, and angular fluxes. Standard interface input files for S/sub N/ constants, inhomogeneous sources, cross sections, and the scalar flux may be read. Flexible edit options as well as a dump and restart capability are provided.
Download or read book Numerical Methods in the Theory of Neutron Transport written by Guriĭ Ivanovich Marchuk and published by Harwood Academic Publishers. This book was released on 1986 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Discrete Ordinates Angular Quadrature of the Neutron Transport Equation written by Kaye D. Lathrop and published by . This book was released on 1965 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Energy Research Abstracts written by and published by . This book was released on 1993 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Rapidly Converging Alternative to Source Iteration for Solving the Discrete Ordinates Radiation Transport Equations in Slab Geometry written by Nicholas J. Wager and published by . This book was released on 2004-03 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: I present a numerical technique to solve the time independent Boltzmann Transport Equation for the transport of neutrons and photons. The technique efficiently solves the discrete ordinates equations with a new iteration scheme. I call this new scheme the angle space distribution iteration method because it combines a non-linear, high angular-resolution flux approximation within individual spatial cells with a coarse angular-resolution flux approximation that couples all cells in a spatial mesh. This shown to be an efficient alternative to source iteration. The new method is implemented using the step characteristic and exponential characteristic spatial quadrature schemes. The latter was introduced in 1993 and has been shown to accurate for both optically thin and optically thick spatial meshes and to produce strictly positive angular fluxes. The discrete ordinates equations can be solved using the conventional source iteration method. However, it is well known that this method converges prohibitively slowly for optically-thick problems with regions that are dominated by scattering rather than absorption. The new scheme converges rapidly even for such problems. Numerical results show that the new scheme is reliably accurate for the problems intended, and that it is fast and efficient in use of memory. The angle space distribution iteration method is demonstrated in slab geometry, for a single energy group, using isotropic cross sections, with exponential and step characteristic spatial quadrature.
Download or read book Variational Nodal Transport Methods for Hexagonal and Three dimensional Geometries Final Report written by and published by . This book was released on 1992 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Method of Moments for Solving the Neutron Transport Equation written by Bengt G. Carlson and published by . This book was released on 1965 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt:
