Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-24T06:26:28.737Z Has data issue: false hasContentIssue false
  • English
  • Français

Parallel Algorithms and Software for Nuclear, Energy, and Environmental Applications. Part I: Multiphysics Algorithms

Published online by Cambridge University Press:  20 August 2015

Derek Gaston ,
Luanjing Guo ,
Glen Hansen ,
Hai Huang ,
Richard Johnson ,
Dana Knoll ,
Chris Newman ,
Hyeong Kae Park ,
Robert Podgorney  and
Michael Tonks
...Show all authors
Derek Gaston*
Affiliation:
Nuclear Science and Technology, Idaho National Laboratory, Idaho Falls, ID 83415, USA
Luanjing Guo*
Affiliation:
Energy and Environment Science and Technology, Idaho National Laboratory, Idaho Falls, ID 83415, USA
Glen Hansen*
Affiliation:
Multiphysics Simulation Technologies Dept. (1444), Sandia National Laboratories, Albuquerque, NM 87185, USA
Hai Huang*
Affiliation:
Energy and Environment Science and Technology, Idaho National Laboratory, Idaho Falls, ID 83415, USA
Richard Johnson*
Affiliation:
Nuclear Science and Technology, Idaho National Laboratory, Idaho Falls, ID 83415, USA
Dana Knoll*
Affiliation:
Fluid Dynamics and Solid Mechanics Group (T-3), Los Alamos National Laboratory, Los Alamos, NM 87545, USA
Chris Newman*
Affiliation:
Fluid Dynamics and Solid Mechanics Group (T-3), Los Alamos National Laboratory, Los Alamos, NM 87545, USA
Hyeong Kae Park*
Affiliation:
Fluid Dynamics and Solid Mechanics Group (T-3), Los Alamos National Laboratory, Los Alamos, NM 87545, USA
Robert Podgorney*
Affiliation:
Energy and Environment Science and Technology, Idaho National Laboratory, Idaho Falls, ID 83415, USA
Michael Tonks*
Affiliation:
Nuclear Science and Technology, Idaho National Laboratory, Idaho Falls, ID 83415, USA
Richard Williamson*
Affiliation:
Nuclear Science and Technology, Idaho National Laboratory, Idaho Falls, ID 83415, USA
*
Email:[email protected]
Email:[email protected]
Corresponding author.Email:[email protected]
Email:[email protected]
Email:[email protected]
Email:[email protected]
Email:[email protected]
Email:[email protected]
Email:[email protected]
Email:[email protected]
Email:[email protected]
Get access

Abstract

There is a growing trend within energy and environmental simulation to consider tightly coupled solutions to multiphysics problems. This can be seen in nuclear reactor analysis where analysts are interested in coupled flow, heat transfer and neutronics, and in nuclear fuel performance simulation where analysts are interested in thermomechanics with contact coupled to species transport and chemistry. In energy and environmental applications, energy extraction involves geomechanics, flow through porous media and fractured formations, adding heat transport for enhanced oil recovery and geothermal applications, and adding reactive transport in the case of applications modeling the underground flow of contaminants. These more ambitious simulations usually motivate some level of parallel computing. Many of the physics coupling efforts to date utilize simple code coupling or first-order operator splitting, often referred to as loose coupling. While these approaches can produce answers, they usually leave questions of accuracy and stability unanswered. Additionally the different physics often reside on distinct meshes and data are coupled via simple interpolation, again leaving open questions of stability and accuracy.

Keywords

65M1265M6065Y0565Z0565H10Multiphysics simulationJacobian-free Newton Krylovfinite element applicationsphysics-based preconditioning
Type
Research Article
Information
Communications in Computational Physics , Volume 12 , Issue 3 , September 2012 , pp. 807 - 833
Copyright
Copyright © Global Science Press Limited 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Gaston, D., Guo, L., Hansen, G., Huang, H., Johnson, R., Knoll, D., Newman, C., Park, H., Podgorney, R., Tonks, M., Williamson, R., Parallel algorithms and software for nuclear, energy, and environmental applications. Part II: Multiphysics softwar, Commun. Comput. Phys. 12 (2012) 834–865.CrossRefGoogle Scholar
[2]Knoll, D. A., Chacon, L., Margolin, L. G., Mousseau, V. A., On balanced approximations for time integration of multiple time scales systems, J. Comput. Phys. 185 (2003) 583–611.Google Scholar
[3]Ropp, D. L., Shadid, J. N., Stability of operator splitting methods for systems with indefinite operators: Reaction-diffusion systems, J. Comput. Phys. 203 (2) (2005) 449–466.Google Scholar
[4]Knoll, D. A., Keyes, D. E., Jacobian-free Newton-Krylov methods: a survey of approaches and applications, J. Comput. Phys. 193 (2) (2004) 357–397.CrossRefGoogle Scholar
[5]Gaston, D., Newman, C., Hansen, G., Lebrun-Grandié, D., MOOSE: A parallel computational framework for coupled systems of nonlinear equations, Nucl. Engrg. Design 239 (2009) 1768–1778.CrossRefGoogle Scholar
[6]Gaston, D., Hansen, G., Kadioglu, S., Knoll, D., Newman, C., Park, H., Permann, C., Tai-tano, W., Parallel multiphysics algorithms and software for computational nuclear engineering, Journal of Physics: Conference Series 180 (1) (2009) 012012.Google Scholar
[7]Park, H., Knoll, D. A., Gaston, D. R., Martineau, R. C., Tightly coupled multiphysics algorithms for pebble bed reactors, Nuclear Science and Engineering 166 (2) (2010) 118–133.Google Scholar
[8]Griffiths, D. F., Sanz-Serna, J., On the scope of the method of modified equations, SIAM J. Sci. Statist. Comput. (1986) 994–1008.Google Scholar
[9] Argonne code center: Benchmark problem book, ANL-7416 supplement 2, Argonne National Laboratory (1977).Google Scholar
[10]Xu, T., Sonnenthal, E. L., Spycher, N., Pruess, K., TOUGHREACT user’s guide: A simulation program for non-isothermal multiphase reactive geochemical transport in variable saturated geologic media, Tech. Rep. LBNL-55460, Berkeley National Laboratory, Berkeley, California (2004).Google Scholar
[11]White, M. D., McGrail, B. P., STOMP (Subsurface Transport over Multiple Phases) version 1.0 addendum: Eckechem equilibrium-conservation-kinetic equation chemistry and reactive transport, Tech. Rep. PNNL-15482, Pacific Northwest National Laboratory, Richland, Washington (2005).Google Scholar
[12]Ropp, D. L., Shadid, J. N., Ober, C. C., Studies of the accuracy of time integration methods for reaction-diffusion equations, J. Comput. Phys. 194 (2) (2004) 544–574.Google Scholar
[13]Estep, D., Ginting, V., Ropp, D., Shadid, J. N., Tavener, S., An A posteriori-A priori analysis of multiscale operator splitting, SIAM J. Numer. Anal. 46 (3) (2008) 116–1146.Google Scholar
[14]Puso, M. A., Laursen, T. A., Mesh tying on curved interfaces in 3D, Engineering Computations 20 (3) (2003) 305–319.Google Scholar
[15]Gee, M. W., Hansen, G. A., Andrs, D., Moertel mortar methods package, http://trilinos.sandia.gov/packages/moertel.Google Scholar
[16]Solin, P., Cerveny, J., Dubcova, L., Dolezel, I., Multi-mesh hp-FEM for thermally conductive incompressible flow, in: M. Papadrakakis, E. Onate, B.Schrefler (Eds.), ECCOMAS Conference on Coupled Problems, CIMNE, Barcelona, 2007, pp. 547–550.Google Scholar
[17]Solin, P., Cerveny, J., Dubcova, L., Adaptive multi-mesh hp-FEM for linear thermoelasticity, Tech. rep., Department of Mathematical Sciences, UTEP, research report No. 2007-08 (2008).Google Scholar
[18]Solin, P., Dubcova, L., Kruis, J., Adaptive hp-FEM with dynamical meshes for transient heat and moisture transfer problems, J. Comput. Appl. Math. 233 (2010) 3103–3112.Google Scholar
[19]Solin, P., Cerveny, J., Dubcova, L., Andrs, D., Monolithic discretization of linear thermoelastic-ity problems via adaptive multimesh hp-FEM, J. Comput. Appl. Math. 234 (2010) 2350–2357.Google Scholar
[20]Dubcova, L., Solin, P., Hansen, G., Park, H., Comparison of multimesh hp-FEMto interpolation and projection methods for spatial coupling of thermal and neutron diffusion calculations, J. Comput. Phys. 230 (4) (2011) 1182–1197.Google Scholar
[21]Jaiman, R. K., Jiao, X., Geubelle, , H., P., Loth, E., Assessment of conservative load transfer for fluid-solid interface with non-matching meshes, Internat. J. Numer. Methods Engrg. 65 (15) (2005) 2014–2038.Google Scholar
[22]Jiao, X., Heath, M. T., Common-refinement-based data transfer between non-matching meshes in multiphysics simulations, Internat. J. Numer. Methods Engrg. 61 (14) (2004) 2402–2427.Google Scholar
[23]Grandy, J., Conservative remapping and region overlays by intersecting arbitrary polyhedra, J. Comput. Phys. 148 (1999) 433–466.Google Scholar
[24]Johnson, R. W., Hansen, G., Newman, C., The role of data transfer on the selection of a single vs. multiple mesh architecture for tightly coupled multiphysics applications, Appl. Math. Comput. 217 (2011) 8943–8962.Google Scholar
[25]Prigogine, I., Lefever, R., Symmetry breaking instabilities in dissipative systems. II, J. Chem. Phys. 48 (4) (1967) 1695–1700.Google Scholar
[26]Wang, Y., Ragusa, J., Application of hp adaptivity to the multigroup diffusion equations, Nuclear Science and Engineering 161 (2009) 22–48.Google Scholar
[27]Solin, P., Segeth, K., Dolezel, I., Higher-Order Finite Element Methods, Chapman & Hall⁄CRC Press, Philadelphia, PA, 2003.Google Scholar
[28]Hansen, G., Owen, S., Mesh generation technology for nuclear reactor simulation; barriers and opportunities, Nucl. Engrg. Design 238 (10) (2008) 2590–2605.Google Scholar
[29]Berndt, M., Moulton, J. D., Hansen, G., Efficient nonlinear solvers for Laplace-Beltrami smoothing of three-dimensional unstructured grids, Comput. Math. Appl. 55 (12) (2008) 2791–2806.Google Scholar
[30]Bates, J. W., Knoll, D. A., On consistent time integration methods for radiation hydrodynamics in the equilibrium diffusion limit: Low energy density regime, J. Comput. Phys. 167 (2001) 99–130.CrossRefGoogle Scholar
[31]Knoll, D., Park, R., Smith, K., Application of the Jacobian-free Newton-Krylov method in computational reactor physics, in: American Nuclear Society 2009 International Conference on Advances in Mathematics, Computational Methods, and Reactor Physics, Saratoga Springs, NY, 2009.Google Scholar
[32]Tonks, M. R., Hansen, G., Gaston, D., Permann, C., Millett, P., Wolf, D., Fully-coupled engineering and mesoscale simulations of thermal conductivity in UO2 fuel using an implicit multiscale approach, Journal of Physics: Conference Series 180 (1) (2009) 012078.Google Scholar
[33]Tonks, M., Gaston, D., Permann, C., Millett, P., Hansen, G., Wolf, D., A coupling methodology for mesoscale-informed nuclear fuel performance codes, Nucl. Engrg. Design 240 (10) (2010) 2877–2883.Google Scholar
[34]Saad, Y., Iterative Methods for Sparse Linear Systems, The PWS Series in Computer Science, PWS Publishing Company, Boston, MA, 1995.Google Scholar
[35]Brown, P. N., Saad, Y., Hybrid Krylov methods for nonlinear systems of equations, SIAM J. Sci. Statist. Comput. 11 (3) (1990) 450–481.Google Scholar
[36]Chan, T. F., Jackson, K. R., Nonlinearly preconditioned Krylov subspace methods for discrete Newton algorithms, SIAM J. Sci. Statist. Comput. 5 (3) (1984) 533–542.Google Scholar
[37]Alur, D., Malks, D., Crupi, J., Core J2EE Patterns: Best Practices and Design Strategies, 2nd Edition, Prentice Hall, New Jersey, USA, 2003.Google Scholar
[38]Dembo, R. S., Eisenstat, S. C., Steihaug, T., Inexact Newton methods, SIAM J. Numer. Anal. 19 (1982) 400–408.Google Scholar
[39]McHugh, P. R., Knoll, D. A., Inexact Newton’s method solutions to the incompressible Navier-Stokes and energy equations using standard and matrix-free implementations, AIAA J. 32 (1994) 2394.Google Scholar
[40]Hansen, G. A., Douglass, R. W., Zardecki, A., Mesh Enhancement: Selected Elliptic Methods, Foundations, and Applications, Research monograph, Imperial College Press, London, UK, 2005.Google Scholar
[41]Heroux, M., et al., Trilinos: an object-oriented software framework for the solution of large-scale, complex multi-physics engineering and scientific problems, http://trilinos.sandia.gov (2008).Google Scholar
[42]Heroux, M. A., Bartlett, R. A., Howle, V. E., Hoekstra, R. J., Hu, J. J., Kolda, T. G., Lehoucq, R. B., Long, K. R., Pawlowski, R. P., Phipps, E. T., Salinger, A. G., Thornquist, H. K., Tuminaro, R. S., Willenbring, J. M., Williams, A., Stanley, K. S., An overview of the trilinos project, ACM Trans. Math. Softw. 31 (3) (2005) 397–423.Google Scholar
[43]Hansen, G., Zardecki, A., Greening, D., Bos, R., A finite element method for three-dimensional unstructured grid smoothing, J. Comput. Phys. 202 (1) (2005) 281–297.Google Scholar
[44]Chacon, L., Lapenta, G., A fully implicit, nonlinear adaptive grid strategy, J. Comput. Phys. 212 (2) (2006) 703–717.Google Scholar
[45]Allison, C. M., Berna, G. A., Chambers, R., Coryell, E. W., Davis, K. L., Hagrman, D. L., Hagrman, D. T., Hampton, N. L., Hohorst, J. K., Mason, R. E., McComas, M. L., McNeil, K. A., Miller, R. L., Olsen, C. S., Reymann, G. A., Siefken, L. J., SCDAP/RELAP5/MOD3.1 code manual, volume IV: MATPRO–A library of materials properties for light-water-reactor accident analysis, Tech. rep., NUREG/CR-6150, EGG-2720 (1993).Google Scholar
[46]Bochev, P., Christon, M., Collis, S., Lehoucq, R., Shadid, J., Slepoy, A., Wagner, G., A mathematical framework for multiscale science and engineering: the variational multiscale method and interscale transfer operators, Tech. Rep. SAND2004-2871, Sandia National Laboratories (Jun. 2004).Google Scholar
[47]Yu, Q., Fish, J., Multiscale asymptotic homogenization for multiphysics problems with multiple spatial and temporal scales: a coupled thermo-viscoelastic example problem, Int. J. of Solids and Structures 39 (2002) 6429–6452.Google Scholar
[48]Michopoulos, J., Farhat, C., Fish, J., Modeling and simulation of multiphysics systems, J. Comput. Inf. Sci. Eng. 5 (3) (2005) 198.Google Scholar
[49]Newman, C., Hansen, G., Gaston, D., Three dimensional coupled simulation of thermome-chanics, heat, and oxygen diffusion in UO2 nuclear fuel rods, Journal of Nuclear Materials 392 (2009) 6–15.Google Scholar
[50]Wagner, G., Liu, W., Coupling of atomistic and continuum simulations using a bridging scale decomposition, J. Comput. Phys. 190 (2003) 249–274.Google Scholar
[51]Millett, P. C., Wolf, D., Desai, T. D., Rokkam, S., El-Azab, A., Phase-field simulation of thermal conductivity in porous polycrystalline microstructres, J. Appl. Phys. 104 (2008) 033512.Google Scholar