A Newton solution for the Superhomogenization method: The PJFNK-SPH
Abstract
This work presents two novel topics regarding the Superhomogenization method: 1) the formalism for the implementation of the method with the linear Boltzmann Transport Equation, and 2) a Newton algorithm for the solution of the nonlinear problem that arises from the method. These new ideas have been implemented in a continuous finite element discretization in the MAMMOTH reactor physics application. The traditional solution strategy for this nonlinear problem uses a Picard, fixed-point iterative process whereas the new implementation relies on MOOSE’s Preconditioned Jacobian-Free Newton Krylov method to allow for a direct solution. The PJFNK-SPH can converge problems that were either intractable or very difficult to converge with the traditional iterative approach, including geometries with reflectors and vacuum boundary conditions. This is partly due to the underlying Scalable Nonlinear Equations Solvers in PETSc, which are integral to MOOSE and offer Newton damping, line search and trust region methods. The PJFNK-SPH has been implemented and tested for various discretizations of the transport equation included in the Rattlesnake transport solver. Speedups of five times for diffusion and ten to fifteen times for transport were obtained when compared to the traditional Picard approach. The three test problems cover a wide range of applications includingmore »
- Publication Date:
- Research Org.:
- Idaho National Lab. (INL), Idaho Falls, ID (United States); Idaho National Laboratory (INL), Idaho Falls, ID (United States)
- Sponsoring Org.:
- USDOE Office of Nuclear Energy (NE)
- OSTI Identifier:
- 1631369
- Alternate Identifier(s):
- OSTI ID: 1469340; OSTI ID: 1476738
- Report Number(s):
- INL/JOU-17-41953-Rev000
Journal ID: ISSN 0306-4549; S0306454917303079; PII: S0306454917303079
- Grant/Contract Number:
- DEAC07-05ID14517; AC07-05ID14517
- Resource Type:
- Published Article
- Journal Name:
- Annals of Nuclear Energy
- Additional Journal Information:
- Journal Name: Annals of Nuclear Energy Journal Volume: 111 Journal Issue: C; Journal ID: ISSN 0306-4549
- Publisher:
- Elsevier
- Country of Publication:
- United Kingdom
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 22 GENERAL STUDIES OF NUCLEAR REACTORS; Superhomogenization; equivalence; homogenization; Rattlesnake; PJFNK; MOOSE; MAMMOTH
Citation Formats
Ortensi, Javier, Wang, Yaqi, Laurier, Alexandre, Schunert, Sebastian, Hébert, Alain, and DeHart, Mark. A Newton solution for the Superhomogenization method: The PJFNK-SPH. United Kingdom: N. p., 2018.
Web. doi:10.1016/j.anucene.2017.09.027.
Ortensi, Javier, Wang, Yaqi, Laurier, Alexandre, Schunert, Sebastian, Hébert, Alain, & DeHart, Mark. A Newton solution for the Superhomogenization method: The PJFNK-SPH. United Kingdom. https://doi.org/10.1016/j.anucene.2017.09.027
Ortensi, Javier, Wang, Yaqi, Laurier, Alexandre, Schunert, Sebastian, Hébert, Alain, and DeHart, Mark. Mon .
"A Newton solution for the Superhomogenization method: The PJFNK-SPH". United Kingdom. https://doi.org/10.1016/j.anucene.2017.09.027.
@article{osti_1631369,
title = {A Newton solution for the Superhomogenization method: The PJFNK-SPH},
author = {Ortensi, Javier and Wang, Yaqi and Laurier, Alexandre and Schunert, Sebastian and Hébert, Alain and DeHart, Mark},
abstractNote = {This work presents two novel topics regarding the Superhomogenization method: 1) the formalism for the implementation of the method with the linear Boltzmann Transport Equation, and 2) a Newton algorithm for the solution of the nonlinear problem that arises from the method. These new ideas have been implemented in a continuous finite element discretization in the MAMMOTH reactor physics application. The traditional solution strategy for this nonlinear problem uses a Picard, fixed-point iterative process whereas the new implementation relies on MOOSE’s Preconditioned Jacobian-Free Newton Krylov method to allow for a direct solution. The PJFNK-SPH can converge problems that were either intractable or very difficult to converge with the traditional iterative approach, including geometries with reflectors and vacuum boundary conditions. This is partly due to the underlying Scalable Nonlinear Equations Solvers in PETSc, which are integral to MOOSE and offer Newton damping, line search and trust region methods. The PJFNK-SPH has been implemented and tested for various discretizations of the transport equation included in the Rattlesnake transport solver. Speedups of five times for diffusion and ten to fifteen times for transport were obtained when compared to the traditional Picard approach. The three test problems cover a wide range of applications including a standard Pressurized Water Reactor lattice with control rods, a Transient Reactor Test facility control rod supercell and a prototype fast-thermal reactor. The reference solutions and initial cross sections were obtained from the Serpent 2 Monte Carlo code. The SPH-corrected cross sections yield eigenvalues that are near exact, relative to reference solutions, for reflected geometries, even with reflector regions. In geometries with vacuum boundary conditions the accuracy is problem dependent and solutions can be within a few to a few hundred pcm. The root-mean-square error in the power distribution is below 0.8% of the reference Monte Carlo. There is little benefit from SPH-corrected transport in typical scoping calculations, but for more detailed analyses it can yield superior convergence of the solution in some of the test problems. This PJFNK-SPH approach is currently being used in the modeling of the Transient Test Reactor at Idaho National Laboratory, where full reactor core SPH-corrected cross sections are employed to reduce the homogenization errors in transient or multi- physics calculations. This base implementation of the PJFNK-SPH provides an extremely robust solver and a springboard to further improve the Superhomogenization method in order to better preserve neutron currents, one of the primary deficiencies of the method.},
doi = {10.1016/j.anucene.2017.09.027},
journal = {Annals of Nuclear Energy},
number = C,
volume = 111,
place = {United Kingdom},
year = {Mon Jan 01 00:00:00 EST 2018},
month = {Mon Jan 01 00:00:00 EST 2018}
}
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1016/j.anucene.2017.09.027
https://doi.org/10.1016/j.anucene.2017.09.027
Other availability
Search WorldCat to find libraries that may hold this journal
Cited by: 18 works
Citation information provided by
Web of Science
Web of Science
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Multidimensional multiphysics simulation of nuclear fuel behavior
journal, April 2012
- Williamson, R. L.; Hales, J. D.; Novascone, S. R.
- Journal of Nuclear Materials, Vol. 423, Issue 1-3
A Consistent Technique for the Pin-by-Pin Homogenization of a Pressurized Water Reactor Assembly
journal, March 1993
- Hébert, A.
- Nuclear Science and Engineering, Vol. 113, Issue 3
Assembly homogenization techniques for light water reactor analysis
journal, January 1986
- Smith, K. S.
- Progress in Nuclear Energy, Vol. 17, Issue 3
Improvement of the SPH Method for Pin-by-Pin Core Calculations
journal, December 2004
- Yamamoto, Akio; Tatsumi, Masahiro; Kitamura, Yasunori
- Journal of Nuclear Science and Technology, Vol. 41, Issue 12
On the use of the SPH method in nodal diffusion analyses of SFR cores
journal, November 2015
- Nikitin, E.; Fridman, E.; Mikityuk, K.
- Annals of Nuclear Energy, Vol. 85
Development of a Third-Generation Superhomogénéisation Method for the Homogenization of a Pressurized Water Reactor Assembly
journal, October 1993
- Hébert, A.; Mathonnière, G.
- Nuclear Science and Engineering, Vol. 115, Issue 2
Application of correction technique using leakage index combined with SPH or discontinuity factors for energy collapsing on pin-by-pin BWR core analysis
journal, August 2014
- Fujita, Tatsuya; Endo, Tomohiro; Yamamoto, Akio
- Journal of Nuclear Science and Technology, Vol. 52, Issue 3
Super-homogenisation factors in pinwise calculations by the reactor dynamics code DYN3D
journal, October 2011
- Grundmann, U.; Mittag, S.
- Annals of Nuclear Energy, Vol. 38, Issue 10
Jacobian-free Newton–Krylov methods: a survey of approaches and applications
journal, January 2004
- Knoll, D. A.; Keyes, D. E.
- Journal of Computational Physics, Vol. 193, Issue 2
A note on application of superhomogénéisation factors to integro-differential neutron transport equations
journal, February 2012
- Chiba, Go; Tsuji, Masashi; Sugiyama, Ken-ichiro
- Journal of Nuclear Science and Technology, Vol. 49, Issue 2
A Consistent Technique for the Global Homogenization of a Pressurized Water Reactor Assembly
journal, December 1991
- Hébert, Alain; Benoist, Pierre
- Nuclear Science and Engineering, Vol. 109, Issue 4
An improved assembly homogenization approach for plate-type research reactor
journal, November 2015
- Ma, Jimin; Wang, Guanbo; Yuan, Shu
- Annals of Nuclear Energy, Vol. 85
MOOSE: A parallel computational framework for coupled systems of nonlinear equations
journal, October 2009
- Gaston, Derek; Newman, Chris; Hansen, Glen
- Nuclear Engineering and Design, Vol. 239, Issue 10