×

A parallel multi-domain solution methodology applied to nonlinear thermal transport problems in nuclear fuel pins. (English) Zbl 1351.80013

Summary: This paper describes an efficient and nonlinearly consistent parallel solution methodology for solving coupled nonlinear thermal transport problems that occur in nuclear reactor applications over hundreds of individual 3D physical subdomains. Efficiency is obtained by leveraging knowledge of the physical domains, the physics on individual domains, and the couplings between them for preconditioning within a Jacobian Free Newton Krylov method. Details of the computational infrastructure that enabled this work, namely the open source Advanced Multi-Physics (AMP) package developed by the authors is described. Details of verification and validation experiments, and parallel performance analysis in weak and strong scaling studies demonstrating the achieved efficiency of the algorithm are presented. Furthermore, numerical experiments demonstrate that the preconditioner developed is independent of the number of fuel subdomains in a fuel rod, which is particularly important when simulating different types of fuel rods. Finally, we demonstrate the power of the coupling methodology by considering problems with couplings between surface and volume physics and coupling of nonlinear thermal transport in fuel rods to an external radiation transport code.

MSC:

80M10 Finite element, Galerkin and related methods applied to problems in thermodynamics and heat transfer
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
80A20 Heat and mass transfer, heat flow (MSC2010)
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[2] Berna, G. A.; Beyer, C. E.; Davis, K. L.; Lanning, D. D., FRAPCON-3: a computer code for the calculation of steady-state, thermal-mechanical behavior of oxide fuel rods for high burnup (1997), Pacific Northwest National Laboratory, Tech. Rep. NUREG/CR-6534
[3] Lyon, W. F.; Jahingir, M. N.; Montgomery, R. O., Fuel analysis and licensing code: FALCON MOD01, vol. 3: verification and validation (2004), EPRI: EPRI Palo Alto, CA, Tech. Rep. 1011309
[4] Newman, C.; Hansen, G.; Gaston, D., Three dimensional coupled simulation of thermomechanics, heat, and oxygen diffusion in \(UO_2\) nuclear fuel rods, J. Nucl. Mater., 392, 1, 6-15 (2009)
[8] Olander, D., Fundamental Aspects of Nuclear Reactor Fuel Elements: Solutions to Problems (1976), Technical Information Center, Office of Public Affairs, Energy Research and Development Administration: Technical Information Center, Office of Public Affairs, Energy Research and Development Administration Berkeley, CA
[9] Phillippe, A., A validation study of the AMP nuclear fuel performance code (2012), University of Tennessee-Knoxville, Master’s thesis
[10] Phillippe, A. M.; Clarno, K. T.; Banfield, J. E.; Ott, L. J.; Philip, B.; Berrill, M. A.; Sampath, R. S.; Allu, S.; Hamilton, S. P., A validation study of pin heat transfer for UO2 fuel based on the IFA-432 experiments, Nucl. Sci. Eng., 177, 275-290 (2014)
[11] Phillippe, A. M.; Clarno, K. T.; Banfield, J. E.; Ott, L. J.; Philip, B.; Berrill, M. A.; Sampath, R. S.; Allu, S.; Hamilton, S. P., A validation study of pin heat transfer for MOX fuel based on the IFA-597 experiments, Nucl. Sci. Eng., 178, 172-185 (2014)
[12] Knoll, D. A.; Keyes, D. E., Jacobian-free Newton-Krylov methods: a survey of approaches and applications, J. Comput. Phys., 193, 357-397 (2004) · Zbl 1036.65045
[13] Dembo, R. S.; Eisenstat, S. C.; Steihaug, T., Inexact Newton methods, SIAM J. Numer. Anal., 19, 400-408 (1982) · Zbl 0478.65030
[14] Eisenstat, S. C.; Walker, H. F., Globally convergent inexact Newton methods, SIAM J. Optim., 4, 393-422 (1994) · Zbl 0814.65049
[15] Kelley, C. T., Iterative Methods for Linear and Nonlinear Equations (1995), SIAM: SIAM Philadelphia · Zbl 0832.65046
[16] Pernice, M.; Walker, H. F., Nitsol: a Newton iterative solver for nonlinear systems, SIAM J. Sci. Comput., 19, 1, 302-318 (1998) · Zbl 0916.65049
[17] Saad, Y.; Schultz, M., GMRES: a generalized minimal residual algorithm for solving non-symmetric linear systems, SIAM J. Sci. Stat. Comput., 7, 856-869 (1986) · Zbl 0599.65018
[18] McHugh, P.; Knoll, D., Comparison of standard and matrix-free implementations of several Newton-Krylov solvers, AIAA J., 32, 12, 2394-2400 (1994) · Zbl 0832.76071
[19] Knoll, D.; McHugh, P., Enhanced nonlinear iterative techniques applied to a nonequilibrium plasma flow, SIAM J. Sci. Comput., 19, 1, 291-301 (1998) · Zbl 0913.76067
[20] Clarno, K. T.; Philip, B.; Cochran, W. K.; Sampath, R. S.; Allu, S.; Barai, P.; Simunovic, S.; Ott, L. J.; Pannala, S.; Nukala, P.; Dilts, G. A.; Mihaila, B.; Unal, C.; Yesilyurt, G.; Lee, J. H.; Banfield, J. E.; Maldonado, G. I., The AMP (Advanced Multi-Physics) nuclear fuel performance code (2011), Oak Ridge National Laboratory, Tech. Rep. ORNL/TM-2011/42
[21] Clarno, K. T.; Philip, B.; Cochran, W. K.; Sampath, R. S.; Allu, S.; Barai, P.; Simunovic, S.; Berrill, M. A.; Ott, L. J.; Pannala, S.; Dilts, G. A.; Mihaila, B.; Yesilyurt, G.; Lee, J. H.; Banfield, J. E., The AMP (Advanced MultiPhysics) nuclear fuel performance code, Nucl. Eng. Des., 252, 108-120 (2012)
[22] Kirk, B. S.; Peterson, J. W.; Stogner, R. H.; Carey, G. F., LibMesh: a C++ library for parallel adaptive mesh refinement/coarsening simulations, Eng. Comput., 22, 3-4, 237-254 (2006)
[25] Heroux, M.; Bartlett, R.; Hoekstra, V. H.R.; Hu, J.; Kolda, T.; Lehoucq, R.; Long, K.; Pawlowski, R.; Phipps, E.; Salinger, A.; Thornquist, H.; Tuminaro, R.; Willenbring, J.; Williams, A., An overview of Trilinos (2003), Sandia National Laboratories, Tech. Rep. SAND2003-2927
[26] Balay, S.; Buschelman, K.; Gropp, W. D.; Kaushik, D.; Knepley, M. G.; McInnes, L. C.; Smith, B. F.; Zhang, H., PETSc home page (2001)
[28] Eisenstat, S. C.; Walker, H. F., Choosing the forcing terms in an inexact Newton method, SIAM J. Sci. Comput., 17, 1, 16-32 (1996) · Zbl 0845.65021
[32] Schubert, A.; Uffelen, P. V.; de Laar, J. V.; Walker, C.; Haeck, W., Extension of the transuranus burn-up model, J. Nucl. Mater., 376, 1-10 (2008)
[33] Childs, H.; Brugger, E. S.; Bonnell, K. S.; Meredith, J. S.; Miller, M.; Whitlock, B. J.; Max, N., A contract-based system for large data visualization, (Proceedings of IEEE Visualization 2005 (2005)), 190-198
[34] Lustre filesystem
[35] Evans, T.; Stafford, A.; Slaybaugh, R.; Clarno, K., DENOVO: a new three-dimensional parallel discrete ordinates code in SCALE, Nucl. Technol., 171, 171-200 (2010)
[38] Palmtag, S., Coupled single assembly solution with VERA (problem 6) (2013), Consortium for Advanced Simulation of LWR’s, Tech. Rep. CASL-U-2013-0150-000
[39] SCALE: a comprehensive modeling and simulation suite for nuclear safety analysis and design (2011), Oak Ridge National Laboratory: Oak Ridge National Laboratory Oak Ridge, TN, Tech. Rep. ORNL/TM-2005/39, Version 6.1
[40] Stewart, G. W., A Krylov-Schur algorithm for large eigenproblems, SIAM J. Matrix Anal. Appl., 23, 3, 601-614 (2001) · Zbl 1003.65045
[41] Kochunas, B.; Jabayy, D.; Collins, B.; Downar, T., Coupled single assembly solution with COBRA-TF/MPACT (problem 6) (2013), Consortium for Advanced Simulation of LWR’s, Tech. Rep. CASL-U-2013-0280-000
[42] Rector, D. R.; Wheeler, C. L.; Lombardo, N. J., Cobra-sfs (spent fuel storage): a thermal-hydraulic analysis computer code, vol. 1: mathematical models and solution method (1986), Tech. Rep. PNL-6049-Vol. 1
[43] Lewis, E. E.; Miller, W. F., Computational Methods of Neutron Transport (1993), American Nuclear Society, Inc.: American Nuclear Society, Inc. La Grange Park, IL, USA · Zbl 0594.65096
[44] Jarrell, J.; Evans, T.; Davidson, G.; Godfrey, A., Full core reactor analysis: running Denovo on Jaguar, Nucl. Sci. Eng., 175, 3, 283-291 (2013)
[45] Cuthcart, J. V., Zirconium metal-water oxidation kinetics, IV. Reaction rate studies (1977), Tech. Rep. ORNL/NUREG-1
[46] Perkins, R., The diffusion of oxygen in oxygen stabilized alpha-zirconium and zircaloy-4, J. Nucl. Mater., 73, 20-29 (1978)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.