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 Government reports annual index written by and published by . This book was released on 199? with total page 1082 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Government Reports Annual Index Keyword A L written by and published by . This book was released on 1984 with total page 1092 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 New Insights Into Numerical Solutions of the Even parity Transport Equation in Two dimensional X Y Geometry written by Taewan Noh and published by . This book was released on 1994 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book TIMEX written by and published by . This book was released on 1976 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: TIMEX solves the time-dependent, one-dimensional multigroup transport equation with delayed neutrons in plane, cylindrical, spherical, and two-angle plane geometries. Both regular and adjoint, inhomogeneous and homogeneous problems subject to vacuum, reflective, periodic, white, albedo or inhomogeneous boundary flux conditions are solved. General anisotropic scattering is allowed and anisotropic inhomogeneous sources are permitted. The discrete ordinates approximation for the angular variable is used with the diamond (central) difference approximation for the angular extrapolation in curved geometries. A linear discontinuous finite element representation for the angular flux in each spatial mesh cell is used. The time variable is differenced by an explicit technique that is unconditionally stable so that arbitrarily large time steps can be taken. Because no iteration is performed the method is exceptionally fast in terms of computing time per time step. Two acceleration methods, exponential extrapolation and rebalance, are utilized to improve the accuracy of the time differencing scheme. Variable dimensioning is used so that any combination of problem parameters leading to a container array less than MAXCOR can be accommodated. The running time for TIMEX is highly problem-dependent, but varies almost linearly with the total number of unknowns and time steps. Provision is made for creation of standard interface output files for angular fluxes and angle-integrated fluxes. Five interface units (use of interface units is optional), five output units, and two system input/output units are required. A large bulk memory is desirable, but may be replaced by disk, drum, or tape storage. 13 tables, 9 figures. (auth).
Download or read book User s Guide for TWOHEX written by Wallace F. Walters and published by . This book was released on 1984 with total page 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 Program to Solve the Multigroup Discrete Ordinates Transport Equation in x Y Z Geometry written by and published by . This book was released on 1976 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical formulations and programming algorithms are given for the THREETRAN computer program which solves the discrete ordinates, multigroup transport equation in (x, y, z) geometry. An efficient, flexible, and general data-handling strategy is derived to make use of three hierarchies of storage: small core memory, large core memory, and disk file. Data management, input instructions, and sample problem output are described. A six-group, S4, 18 502 mesh point, 2 800 zone, k/sub eff/ calculation of the ZPPR-4 critical assembly required 144 min of CDC-7600 time to execute to a convergence tolerance of 5 x 10−4 and gave results in good qualitative agreement with experiment and other calculations. 6 references.
Download or read book Linear Characteristic Spatial Quadrature for Discrete Ordinates Neutral Particle Transport on Arbitrary Triangles written by Dennis J. Miller (CAPT, USAF.) and published by . This book was released on 1993 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Characteristic Methods for Solving the Particle Transport Equation in 1 D Spherical Geometry written by and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A family of numerical methods for solving the particle transport equation in 1-D spherical geometry are developed using the method of characteristics. The development of these methods is driven by a desire to: (i) provide solutions to transport problems which cannot otherwise be determined using analytic techniques and (ii) provide comparative solutions to test methods developed for other curvilinear geometries. Problems that are of increasing importance to the transport community are those that contain subdomains which are considered optically thick and diffusive. These problems result in high computational costs due to the grid refinement necessary to generate acceptable solutions. As a result, we look to develop vertex-based characteristic methods that can reproduce these diffusive solutions without resorting to significant spatial grid refinement. This research will allow for continued development of advanced conservative characteristic methods with better properties for R-Z geometries. The transport methods derived here are based on a change of coordinates that removes the angular derivative term in the differential operator resulting in a first order differential equation which can be discretized using methods similar to those found in 1-D slab geometry. In this study, we present a family of characteristic methods; Vladimirov's method of characteristics, a conservative long characteristic method, two locally conservative short characteristic methods, a linear long characteristic method, and an explicit slope long characteristic method. The numerical results presented in this thesis demonstrate the performance of each method. We found that the linear and explicit slope long characteristic methods generated numerical solutions which are well behaved in some diffusive problems. Also, we analyzed several of these methods using asymptotic diffusion limit analysis and found that the linear long characteristic method limits to a discretized version of the diffusion e.
Download or read book Parallel Finite Element Electron Photon Transport Analysis on 2 D Unstructured Mesh written by and published by . This book was released on 1999 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A computer code has been developed to solve the linear Boltzmann transport equation on an unstructured mesh of triangles, from a Pro/E model. An arbitriwy arrangement of distinct material regions is allowed. Energy dependence is handled by solving over an arbitrary number of discrete energy groups. Angular de- pendence is treated by Legendre-polynomial expansion of the particle cross sections and a discrete ordinates treatment of the particle fluence. The resulting linear system is solved in parallel with a preconditioned conjugate-gradients method. The solution method is unique, in that the space-angle dependence is solved si- multaneously, eliminating the need for the usual inner iterations. Electron cross sections are obtained from a Goudsrnit-Saunderson modifed version of the CEPXS code. A one-dimensional version of the code has also been develop@ for testing and development purposes.
Download or read book Numerical Transport Theory Final Report written by and published by . This book was released on 1994 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: The basic problem addressed in the project was that of accelerating the iterative convergence of Discrete Ordinates (S{sub N}) problems. Important previous work on this problem, much of which was done at LANL, has shown that the Diffusion Synthetic Acceleration (DSA) method can be a very effective acceleration procedure. However, in two-dimensional geometries, only the diamond differenced S{sub N} equations have been efficiently solved using DSA. This is because, for the 2-D diamond-differenced S{sub N} equations, the standard DSA procedure leads to a relatively simple discretized low-order diffusion equation that for many problems can be efficiently solved by a multigrid method. For other discretized versions of the S{sub N} equations, the standard DSA procedure leads to much more complicated discretizations of the low-order diffusion equation that have not been efficiently solved by multigrid (or other) methods. In this project, we have developed a new procedure to obtain discretized diffusion equations for DSA-accelerating the convergence of the S{sub N} equations using certain lumped discontinuous finite element spatial differencing methods. The idea is to use an asymptotic analysis for the derivation of the discretized diffusion equation. This is based on the fact that diffusion theory is an asymptotic limit of transport theory. The asymptotic analysis also shows that the schemes considered in this project are highly accurate for diffusive problems with spatial meshes that are optically thick. Specifically, we apply this DSA procedure to a lumped Linear Discontinuous (LD) scheme for slab geometry and a lumped Bilinear Discontinuous (BLD) scheme for x, y-geometry. Our theoretical and numerical results indicate that these schemes are very accurate and can be solved efficiently using the new method. We describe the concept that underlies the DSA method. We describe the basic asymptotic relationship between transport and diffusion theory.
Download or read book Handbook of Nuclear Engineering written by Dan Gabriel Cacuci and published by Springer Science & Business Media. This book was released on 2010-09-14 with total page 3701 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an authoritative compilation of information regarding methods and data used in all phases of nuclear engineering. Addressing nuclear engineers and scientists at all levels, this book provides a condensed reference on nuclear engineering since 1958.
Download or read book Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations written by Beatrice Riviere and published by SIAM. This book was released on 2008-12-18 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focuses on three primal DG methods, covering both theory and computation, and providing the basic tools for analysis.
Download or read book The Physics of Nuclear Reactors written by Serge Marguet and published by Springer. This book was released on 2018-02-26 with total page 1462 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive volume offers readers a progressive and highly detailed introduction to the complex behavior of neutrons in general, and in the context of nuclear power generation. A compendium and handbook for nuclear engineers, a source of teaching material for academic lecturers as well as a graduate text for advanced students and other non-experts wishing to enter this field, it is based on the author’s teaching and research experience and his recognized expertise in nuclear safety. After recapping a number of points in nuclear physics, placing the theoretical notions in their historical context, the book successively reveals the latest quantitative theories concerning: • The slowing-down of neutrons in matter • The charged particles and electromagnetic rays • The calculation scheme, especially the simplification hypothesis • The concept of criticality based on chain reactions • The theory of homogeneous and heterogeneous reactors • The problem of self-shielding • The theory of the nuclear reflector, a subject largely ignored in literature • The computational methods in transport and diffusion theories Complemented by more than 400 bibliographical references, some of which are commented and annotated, and augmented by an appendix on the history of reactor physics at EDF (Electricité De France), this book is the most comprehensive and up-to-date introduction to and reference resource in neutronics and reactor theory.
Download or read book Treatment Planning in Radiation Oncology written by Faiz M. Khan and published by Lippincott Williams & Wilkins. This book was released on 1998 with total page 645 pages. Available in PDF, EPUB and Kindle. Book excerpt: Radiation oncology is integrated with medical physics for a unique look at the state of the art in cancer patient care. World-renowned authors provide a complete discussion of treatment planning featuring the clinical, physical, and technical aspects involved. Coverage includes 3-D conformal treatment and other advancements in computer technology and medical imaging to bring the reader a modern perspective on treatment planning.
