An Analytical Nodal Discrete Ordinates Solution to the Transport Equation in Cartesian Geometry PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download An Analytical Nodal Discrete Ordinates Solution to the Transport Equation in Cartesian Geometry PDF full book. Access full book title An Analytical Nodal Discrete Ordinates Solution to the Transport Equation in Cartesian Geometry by Joshua Rocheleau. Download full books in PDF and EPUB format.
Author: Joshua Rocheleau Publisher: ISBN: Category : Nuclear engineering Languages : en Pages : 88
Book Description
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.
Author: Joshua Rocheleau Publisher: ISBN: Category : Nuclear engineering Languages : en Pages : 88
Book Description
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.
Author: Publisher: ISBN: Category : Languages : en Pages :
Book Description
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: Publisher: ISBN: Category : Languages : en Pages : 11
Book Description
The authors propose a modification of the Arbitrarily High Order Transport Nodal method whereby they solve each node and each direction using different expansion order. With this feature and a previously proposed a posteriori error estimator they develop an adaptive order scheme to automatically improve the accuracy of the solution of the transport equation. They implemented the modified nodal method, the error estimator and the adaptive order scheme into a discrete-ordinates code for solving monoenergetic, fixed source, isotropic scattering problems in two-dimensional Cartesian geometry. They solve two test problems with large homogeneous regions to test the adaptive order scheme. The results show that using the adaptive process the storage requirements are reduced while preserving the accuracy of the results.
Author: Christian Constanda Publisher: Springer Nature ISBN: 303134099X Category : Mathematics Languages : en Pages : 407
Book Description
This volume contains a collection of articles on state-of-the-art developments in the construction of theoretical integral techniques and their application to specific problems in science and engineering. Chapters in this book are based on talks given at the Seventeenth International Conference on Integral Methods in Science and Engineering, held virtually in July 2022, and are written by internationally recognized researchers. This collection will be of interest to researchers in applied mathematics, physics, and mechanical, electrical, and petroleum engineering, as well as graduate students in these disciplines and other professionals for whom integration is an essential working tool.
Author: Publisher: ISBN: Category : Languages : en Pages : 37
Book Description
We have developed and successfully implemented a two-dimensional bilinear discontinuous in space and time, used in conjunction with the S{sub N} angular approximation, to numerically solve the time dependent, one-dimensional, one-speed, slab geometry, (ion) transport equation. Numerical results and comparison with analytical solutions have shown that the bilinear-discontinuous (BLD) scheme is third-order accurate in the space ad time dimensions independently. Comparison of the BLD results with diamond-difference methods indicate that the BLD method is both quantitavely and qualitatively superior to the DD scheme. We note that the form of the transport operator is such that these conclusions carry over to energy dependent problems that include the constant-slowing-down-approximation term, and to multiple space dimensions or combinations thereof. An optimized marching or inversion scheme or a parallel algorithm should be investigated to determine if the increased accuracy can compensate for the extra overhead required for a BLD solution, and then could be compared to other discretization methods such as nodal or characteristic schemes.
Author: Publisher: ISBN: Category : Power resources Languages : en Pages : 586
Book Description
Semiannual, with semiannual and annual indexes. References to all scientific and technical literature coming from DOE, its laboratories, energy centers, and contractors. Includes all works deriving from DOE, other related government-sponsored information, and foreign nonnuclear information. Arranged under 39 categories, e.g., Biomedical sciences, basic studies; Biomedical sciences, applied studies; Health and safety; and Fusion energy. Entry gives bibliographical information and abstract. Corporate, author, subject, report number indexes.
Author: Helcio R.B. Orlande Publisher: CRC Press ISBN: 1439845565 Category : Science Languages : en Pages : 754
Book Description
With its uncommon presentation of instructional material regarding mathematical modeling, measurements, and solution of inverse problems, Thermal Measurements and Inverse Techniques is a one-stop reference for those dealing with various aspects of heat transfer. Progress in mathematical modeling of complex industrial and environmental systems has e
Author: Joshua Rocheleau
Author: Joshua Rocheleau
Author: 
Author: 
Author: Christian Constanda
Author: 
Author: 
Author: Richard R. Paternoster
Author: Helcio R.B. Orlande
Author: 
Author: