A Linear Characteristic-nodal Transport Method for the Two-dimensional (x, Y)-geometry Multigroup Discrete Ordinates Equations Over an Arbitrary Triangle Mesh PDF Download

Author: Richard R. Paternoster
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Category : Boundary value problems
Languages : en
Pages : 256

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Category :
Languages : en
Pages : 1082

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Category : Government reports announcements & index
Languages : en
Pages : 1092

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Languages : en
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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.

Author: Taewan Noh
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Category :
Languages : en
Pages : 244

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Languages : en
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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).

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Languages : en
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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.

Author: Dennis J. Miller (CAPT, USAF.)
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Category : Neutron transport theory
Languages : en
Pages : 242

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Languages : en
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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.

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Languages : en
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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.