General Order Characteristic Methods for Solving Neutron Transport Problems PDF Download
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Author: Publisher: ISBN: Category : Languages : en Pages : 27
Book Description
The neutron transport equation in Cartesian geometry possesses straight line characteristics along which the streaming operator can be written as a full differential in terms of the characteristic length. This idea was used by Lathrop to develop the step characteristic method, which he showed to be positive definite but less accurate than conventional Diamond-Difference schemes. Several authors since then have developed new methods utilizing the characteristic curves (including non-Cartesian geometry). A Linear Characteristic Method, based on a more consistent linear representation of the incoming-surface and within-cell angular flux, has been developed and tested in two-dimensional geometry producing highly accurate and computationally efficient results. A similar linear method, with several modifications, was developed for three-dimensional Cartesian geometry, and implemented in ORNL's production code TORT. In this paper is presented a fully consistent, two-dimensional Cartesian geometry, general order characteristic method, in the same spirit as the previously developed, general order nodal method. Preliminary tests and numerical error analysis of the new method for orders up to five are also presented.
Author: Publisher: ISBN: Category : Languages : en Pages : 27
Book Description
The neutron transport equation in Cartesian geometry possesses straight line characteristics along which the streaming operator can be written as a full differential in terms of the characteristic length. This idea was used by Lathrop to develop the step characteristic method, which he showed to be positive definite but less accurate than conventional Diamond-Difference schemes. Several authors since then have developed new methods utilizing the characteristic curves (including non-Cartesian geometry). A Linear Characteristic Method, based on a more consistent linear representation of the incoming-surface and within-cell angular flux, has been developed and tested in two-dimensional geometry producing highly accurate and computationally efficient results. A similar linear method, with several modifications, was developed for three-dimensional Cartesian geometry, and implemented in ORNL's production code TORT. In this paper is presented a fully consistent, two-dimensional Cartesian geometry, general order characteristic method, in the same spirit as the previously developed, general order nodal method. Preliminary tests and numerical error analysis of the new method for orders up to five are also presented.
Author: Publisher: ISBN: Category : Aeronautics Languages : en Pages : 456
Book Description
Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
Author: Ramadan M. Kuridan Publisher: Springer Nature ISBN: 3031269322 Category : Science Languages : en Pages : 284
Book Description
This textbook provides a thorough explanation of the physical concepts and presents the general theory of different forms through approximations of the neutron transport processes in nuclear reactors and emphasize the numerical computing methods that lead to the prediction of neutron behavior. Detailed derivations and thorough discussions are the prominent features of this book unlike the brevity and conciseness which are the characteristic of most available textbooks on the subject where students find them difficult to follow. This conclusion has been reached from the experience gained through decades of teaching. The topics covered in this book are suitable for senior undergraduate and graduate students in the fields of nuclear engineering and physics. Other engineering and science students may find the construction and methodology of tackling problems as presented in this book appealing from which they can benefit in solving other problems numerically. The book provides access to a one dimensional, two energy group neutron diffusion program including a user manual, examples, and test problems for student practice. An option of a Matlab user interface is also available.
Author: Dan Gabriel Cacuci Publisher: Springer Science & Business Media ISBN: 0387981306 Category : Science Languages : en Pages : 3701
Book Description
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.
Author: Saam Yasseri Publisher: ISBN: Category : Diffusion Languages : en Pages :
Book Description
In this dissertation, three different methods for solving the Boltzmann neutron transport equation (and its low-order approximations) are developed in general geometry and implemented in 1D slab geometry. The first method is for solving the fine-group diffusion equation by estimating the in-scattering and fission source terms with consistent coarse-group diffusion solutions iteratively. This is achieved by extending the subgroup decomposition method initially developed in neutron transport theory to diffusion theory. Additionally, a new stabilizing scheme for on-the-fly cross section re-condensation based on local fixed source calculations is developed in the subgroup decomposition framework. The method is derived in general geometry and tested in 1D benchmark problems characteristic of Boiling Water Reactors (BWR) and Gas Cooled Reactor (GCR). It is shown that the method reproduces the standard fine-group results with 3-4 times faster computational speed in the BWR test problem and 1.5 to 6 times faster computational speed in the GCR core. The second method is a hybrid diffusion transport method for accelerating multi-group eigenvalue transport problems. This method extends the subgroup decomposition method to efficiently couple a coarse-group high-order diffusion method with a set of fixed-source transport decomposition sweeps to obtain the fine-group transport solution. The advantages of this new high-order diffusion theory are its consistent transport closure, straight forward implementation and numerical stability. The method is analyzed for 1D BWR and High Temperature Test Reactor (HTTR) benchmark problems. It is shown that the method reproduces the fine-group transport solution with high accuracy while increasing the computationally efficiency up to 16 times in the BWR core and up to 3.3 times in the HTTR core compared to direct fine-group transport calculations. The third method is a new spatial homogenization method in transport theory that reproduces the heterogeneous solution by using conventional flux weighted homogenized cross sections. By introducing an additional source term via an "auxiliary cross section" the resulting homogeneous transport equation becomes consistent with the heterogeneous equation, enabling easy implementation into existing solution methods/codes. This new method utilizes on-the-fly re-homogenization, performed at the assembly level, to correct for core environment effects on the homogenized cross sections. The method is derived in general geometry and continuous energy, and implemented and tested in fine-group 1D slab geometries typical of BWR and GCR cores. The test problems include two single assembly and 4 core configurations. It is believed that the coupling of the two new methods, namely the hybrid method for treating the energy variable and the new spatial homogenization method in transport theory set the stage, as future work, for the development of a robust and practical method for highly efficient and accurate whole core transport calculations.
Author: Daniele Sciannandrone Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
The topic of our research is the application of the Method of Long Characteristics (MOC) to solve the Neutron Transport Equation in three-dimensional axial geometries. The strength of the MOC is in its precision and versatility. As a drawback, it requires a large amount of computational resources. This problem is even more severe in three-dimensional geometries, for which unknowns reach the order of tens of billions for assembly-level calculations.The first part of the research has dealt with the development of optimized tracking and reconstruction techniques which take advantage of the regularities of three-dimensional axial geometries. These methods have allowed a strong reduction of the memory requirements and a reduction of the execution time of the MOC calculation.The convergence of the iterative scheme has been accelerated with a lower-order transport operator (DPN) which is used for the initialization of the solution and for solving the synthetic problem during MOC iterations.The algorithms for the construction and solution of the MOC and DPN operators have been accelerated by using shared-memory parallel paradigms which are more suitable for standard desktop working stations. An important part of this research has been devoted to the implementation of scheduling techniques to improve the parallel efficiency.The convergence of the angular quadrature formula for three-dimensional cases is also studied. Some of these formulas take advantage of the reduced computational costs of the treatment of planar directions and the vertical direction to speed up the algorithm.The verification of the MOC solver has been done by comparing results with continuous-in-energy Monte Carlo calculations. For this purpose a coupling of the 3D MOC solver with the Subgroup method is proposed to take into account the effects of cross sections resonances. The full calculation of a FBR assembly requires about 2 hours of execution time with differences of few PCM with respect to the reference results.We also propose a higher order scheme of the MOC solver based on an axial polynomial expansion of the unknown within each mesh. This method allows the reduction of the meshes (and unknowns) by keeping the same precision.All the methods developed in this thesis have been implemented in the APOLLO3 version of the neutron transport solver TDT.
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Author: Ramadan M. Kuridan
Author: Dan Gabriel Cacuci
Author: Saam Yasseri
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Author: Guriĭ Ivanovich Marchuk
Author: Bengt G. Carlson
Author: Bengt G. Carlson
Author: Daniele Sciannandrone