TY - GEN
T1 - NUMERICAL CASEOLOGY BY LAGRANGE INTERPOLATION FOR THE 1D NEUTRON TRANSPORT EQUATION IN A SLAB
AU - Ganapol, B. D.
N1 - Publisher Copyright:
Copyright © 2021 AMERICAN NUCLEAR SOCIETY, INCORPORATED, LA GRANGE PARK, ILLINOIS 60526.All rights reserved.
PY - 2021
Y1 - 2021
N2 - Here, we are concerned with a new, highly precise, numerical solution to the 1D neutron transport equation based on Case's analytical solution. While many numerical solutions currently exist, understandably, because of the complexity of the transport equation, even in 1D, there is only one that is truly analytical- Ken Case's singular eigenfunction expansion (SEE). In 1960, Case introduced the SEE for a variety of idealized transport problems and forever changed the landscape of analytical transport theory. Several numerical methods including the CN and FN methods were built upon the core of SEE. What we present is yet another featuring the simplicity and precision of the FN method, but for a more convenient and natural Lagrangian polynomial basis, called the LN method.
AB - Here, we are concerned with a new, highly precise, numerical solution to the 1D neutron transport equation based on Case's analytical solution. While many numerical solutions currently exist, understandably, because of the complexity of the transport equation, even in 1D, there is only one that is truly analytical- Ken Case's singular eigenfunction expansion (SEE). In 1960, Case introduced the SEE for a variety of idealized transport problems and forever changed the landscape of analytical transport theory. Several numerical methods including the CN and FN methods were built upon the core of SEE. What we present is yet another featuring the simplicity and precision of the FN method, but for a more convenient and natural Lagrangian polynomial basis, called the LN method.
KW - Lagrange interpolation
KW - Singular eigenfunctions
KW - Slab transport
UR - http://www.scopus.com/inward/record.url?scp=85183600141&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85183600141&partnerID=8YFLogxK
U2 - 10.13182/M&C21-33729
DO - 10.13182/M&C21-33729
M3 - Conference contribution
AN - SCOPUS:85183600141
T3 - Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021
SP - 1184
EP - 1193
BT - Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021
PB - American Nuclear Society
T2 - 2021 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021
Y2 - 3 October 2021 through 7 October 2021
ER -