Model Reduction for Multiscale Lithium-Ion Battery Simulation

Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 112)

Abstract

In this contribution we are concerned with efficient model reduction for multiscale problems arising in lithium-ion battery modeling with spatially resolved porous electrodes. We present new results on the application of the reduced basis method to the resulting instationary 3D battery model that involves strong non-linearities due to Buttler-Volmer kinetics. Empirical operator interpolation is used to efficiently deal with this issue. Furthermore, we present the localized reduced basis multiscale method for parabolic problems applied to a thermal model of batteries with resolved porous electrodes. Numerical experiments are given that demonstrate the reduction capabilities of the presented approaches for these real world applications.

References

  1. 1.
    F. Albrecht, B. Haasdonk, S. Kaulmann, M. Ohlberger, The localized reduced basis multiscale method, in ALGORITMY 2012 – Proceedings of contributed papers and posters, ed. by A. Handlovicova, Z. Minarechova, D. Cevcovic, vol. 1 (Slovak University of Technology in Bratislava, Publishing House of STU, 2012) pp. 393–403Google Scholar
  2. 2.
    M. Barrault, Y. Maday, N. Nguyen, A. Patera, An “empirical interpolation” method: application to efficient reduced-basis discretization of partial differential equations. Comptes Rendus de l’Académie des Sciences, Series I 339, 667–672 (2004)MathSciNetMATHGoogle Scholar
  3. 3.
    P. Bastian, M. Blatt, A. Dedner, C. Engwer, R. Klöfkorn, R. Kornhuber, M. Ohlberger, O. Sander, A generic grid interface for parallel and adaptive scientific computing. II. Implementation and tests in DUNE. Computing 82 (2–3), 121–138 (2008)MathSciNetMATHGoogle Scholar
  4. 4.
    P. Bastian, M. Blatt, A. Dedner, C. Engwer, R. Klöfkorn, M. Ohlberger, O. Sander, A generic grid interface for parallel and adaptive scientific computing. I. Abstract framework. Computing 82 (2–3), 103–119 (2008)MathSciNetMATHGoogle Scholar
  5. 5.
    L. Cai, R. White, Reduction of model order based on proper orthogonal decomposition for lithium-ion battery simulations. J. Electrochem. Soc. 156 (3), A154–A161, cited By 67 (2009)Google Scholar
  6. 6.
    S.C. Chen, C.C. Wan, Y.Y. Wang, Thermal analysis of lithium-ion batteries. J. Power Sources 140, 111–124 (2005)CrossRefGoogle Scholar
  7. 7.
    F. Ciucci, W. Lai, Derivation of micro/macro lithium battery models from homogenization. Transp. Porous Media 88 (2), 249–270 (2011)MathSciNetCrossRefGoogle Scholar
  8. 8.
    M. Doyle, T. Fuller, J. Newman, Modeling of galvanostatic charge and discharge of the lithium/ polymer/insertion cell. J. Electrochem. Soc. 140 (6), 1526–1533, cited By 789 (1993)Google Scholar
  9. 9.
    M. Drohmann, B. Haasdonk, M. Ohlberger, Reduced basis approximation for nonlinear parametrized evolution equations based on empirical operator interpolation. SIAM J. Sci. Comput. 34 (2), A937–A969 (2012)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    S. Golmon, K. Maute, M.L. Dunn, Multiscale design optimization of lithium ion batteries using adjoint sensitivity analysis. Internat. J. Numer. Methods Eng. 92 (5), 475–494 (2012)MathSciNetCrossRefGoogle Scholar
  11. 11.
    B. Haasdonk, Convergence rates of the POD-Greedy method. M2AN Math. Model. Numer. Anal. 47, 859–873 (2013)Google Scholar
  12. 12.
    B. Haasdonk, Reduced basis methods for parametrized PDEs – A tutorial introduction for stationary and instationary problems, Technical report, 2014, Chapter to appear in P. Benner, A. Cohen, M. Ohlberger and K. Willcox: “Model Reduction and Approximation: Theory and Algorithms”, SIAMGoogle Scholar
  13. 13.
    B. Haasdonk, M. Ohlberger, G. Rozza, A reduced basis method for evolution schemes with parameter-dependent explicit operators. Electron. Trans. Numer. Anal. 32, 145–161 (2008)MathSciNetMATHGoogle Scholar
  14. 14.
    B. Haasdonk, M. Ohlberger, Reduced basis method for finite volume approximations of parametrized linear evolution equations. M2AN Math. Model. Numer. Anal. 42 (2), 277–302 (2008)Google Scholar
  15. 15.
    J.S. Hesthaven, G. Rozza, B. Stamm, SpringerBriefs in Mathematics. (Springer International Publishing, Heidelberg, 2016)Google Scholar
  16. 16.
    O. Iliev, A. Latz, J. Zausch, S. Zhang, On some model reduction approaches for simulations of processes in Li-ion battery, in Proceedings of Algoritmy 2012, Conference on Scientific Computing (Slovak University of Technology in Bratislava, Vysoké Tatry, Podbanské, 2012), pp. 161–171MATHGoogle Scholar
  17. 17.
    S. Kaulmann, B. Flemisch, B. Haasdonk, K.-A. Lie, M. Ohlberger, The localized reduced basis multiscale method for two-phase flows in porous media. Internat. J. Numer. Methods Eng. 102 (5), 1018–1040 (2015)MathSciNetCrossRefGoogle Scholar
  18. 18.
    S. Kaulmann, M. Ohlberger, B. Haasdonk, A new local reduced basis discontinuous Galerkin approach for heterogeneous multiscale problems. C. R. Math. Acad. Sci. Paris 349 (23–24), 1233–1238 (2011)MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    O. Lass, S. Volkwein, Parameter identification for nonlinear elliptic-parabolic systems with application in lithium-ion battery modeling. Comput. Optim. Appl. 62 (1), 217–239 (2015)MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    A. Latz, J. Zausch, Thermodynamic consistent transport theory of Li-ion batteries. J. Power Sources 196 (6), 3296–3302 (2011)CrossRefMATHGoogle Scholar
  21. 21.
    G.B. Less, J.H. Seo, S. Han, A.M. Sastry, J. Zausch, A. Latz, S. Schmidt, C. Wieser, D. Kehrwald, S. Fell, Micro-scale modeling of Li-ion batteries: parameterization and validation. J. Electrochem. Soc. 159 (6), A697 (2012)Google Scholar
  22. 22.
    R. Milk, S. Rave, F. Schindler, pyMOR - generic algorithms and interfaces for model order reduction (2015), arXiv e-prints 1506.07094, http://arxiv.org/abs/1506.07094.
  23. 23.
    R. Milk, F. Schindler, dune-gdt (2015), (http://dx.doi.org/10.5281/zenodo.35389)
  24. 24.
    R. Milk, F. Schindler, dune-stuff (2015), (http://dx.doi.org/10.5281/zenodo.35390)
  25. 25.
    M. Ohlberger, F. Schindler, A-posteriori error estimates for the localized reduced basis multi-scale method, in Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects, ed. by (J. Fuhrmann, M. Ohlberger, C. Rohde. Springer Proceedings in Mathematics & Statistics, vol. 77 (Springer International Publishing, Berlin, 2014), pp. 421–429Google Scholar
  26. 26.
    M. Ohlberger, F. Schindler, Error control for the localized reduced basis multi-scale method with adaptive on-line enrichment. SIAM J. Sci. Comput. 37 (6), A2865–A2895 (2015)MathSciNetCrossRefMATHGoogle Scholar
  27. 27.
    M. Ohlberger, S. Rave, S. Schmidt, S. Zhang, A model reduction framework for efficient simulation of Li-ion batteries, in Finite Volumes for Complex Applications. VII. Elliptic, Parabolic and Hyperbolic Problems. Springer Proceedings in Mathematics & Statistics, vol. 78 (Springer, Cham, 2014), pp. 695–702Google Scholar
  28. 28.
    P. Popov, Y. Vutov, S. Margenov, O. Iliev, Finite volume discretization of equations describing nonlinear diffusion in Li-ion batteries, in Numerical Methods and Applications, ed. by I. Dimov, S. Dimova, N. Kolkovska. Lecture Notes in Computer Science, vol. 6046 (Springer, Berlin/Heidelberg, 2011), pp. 338–346Google Scholar
  29. 29.
    A. Quarteroni, A. Manzoni, F. Negri, Reduced Basis Methods for Partial Differential Equations: An Introduction. Unitext, vol. 92. (Springer, Cham, 2016). La Matematica per il 3+2Google Scholar
  30. 30.
    V. Taralova, Upscaling approaches for nonlinear processes in lithium-ion batteries, Ph.D. thesis, Kaiserslautern, Technische Universität Kaiserslautern, 2015, pp. VII, 224Google Scholar
  31. 31.
    A. Wesche, S. Volkwein, The reduced basis method applied to transport equations of a lithium-ion battery. COMPEL: Int. J. Comput. Math. Electr. Electron. Eng. 32, 1760–1772 (2013)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Mario Ohlberger
    • 1
  • Stephan Rave
    • 1
  • Felix Schindler
    • 1
  1. 1.Applied Mathematics Münster, CMTC & Center for Nonlinear ScienceUniversity of MünsterMünsterGermany

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