Skip to main content
SpringerLink
Log in

Model Reduction for Multiscale Lithium-Ion Battery Simulation

  • Conference paper
  • First Online:
Numerical Mathematics and Advanced Applications ENUMATH 2015

Part of the book series: Lecture Notes in Computational Science and Engineering ((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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    https://github.com/pymor/dune-hdd

  2. 2.

    https://github.com/pymor/dune-pymor

References

  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. 393–403

    Google Scholar 

  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)

    MathSciNet  MATH  Google Scholar 

  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)

    MathSciNet  MATH  Google Scholar 

  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)

    MathSciNet  MATH  Google Scholar 

  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. S.C. Chen, C.C. Wan, Y.Y. Wang, Thermal analysis of lithium-ion batteries. J. Power Sources 140, 111–124 (2005)

    Article  Google Scholar 

  7. F. Ciucci, W. Lai, Derivation of micro/macro lithium battery models from homogenization. Transp. Porous Media 88 (2), 249–270 (2011)

    Article  MathSciNet  Google Scholar 

  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. 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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  11. B. Haasdonk, Convergence rates of the POD-Greedy method. M2AN Math. Model. Numer. Anal. 47, 859–873 (2013)

    Google Scholar 

  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”, SIAM

    Google Scholar 

  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)

    MathSciNet  MATH  Google Scholar 

  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. J.S. Hesthaven, G. Rozza, B. Stamm, SpringerBriefs in Mathematics. (Springer International Publishing, Heidelberg, 2016)

    Google Scholar 

  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. 161–171

    MATH  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  20. A. Latz, J. Zausch, Thermodynamic consistent transport theory of Li-ion batteries. J. Power Sources 196 (6), 3296–3302 (2011)

    Article  MATH  Google Scholar 

  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. 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. R. Milk, F. Schindler, dune-gdt (2015), (http://dx.doi.org/10.5281/zenodo.35389)

  24. R. Milk, F. Schindler, dune-stuff (2015), (http://dx.doi.org/10.5281/zenodo.35390)

  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. 421–429

    Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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. 695–702

    Google Scholar 

  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. 338–346

    Google Scholar 

  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+2

    Google Scholar 

  30. V. Taralova, Upscaling approaches for nonlinear processes in lithium-ion batteries, Ph.D. thesis, Kaiserslautern, Technische Universität Kaiserslautern, 2015, pp. VII, 224

    Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The authors thank Sebastian Schmidt from Fraunhofer ITWM Kaiserslautern for the close and fruitful collaboration within the BMBF-project MULTIBAT towards integration of BEST with pyMOR. This work has been supported by the German Federal Ministry of Education and Research (BMBF) under contract number 05M13PMA.

Author information

Authors and Affiliations

  1. Applied Mathematics Münster, CMTC & Center for Nonlinear Science, University of Münster, Einsteinstr. 62, 48149, Münster, Germany

    Mario Ohlberger, Stephan Rave & Felix Schindler

Authors
  1. Mario Ohlberger
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stephan Rave
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Felix Schindler
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mario Ohlberger .

Editor information

Editors and Affiliations

  1. Mathematics & Applied Mathematics, Middle East Technical University Mathematics & Applied Mathematics, Ankara, Turkey

    Bülent Karasözen

  2. Dept of Computer Engg, Middle East Technical Univ Dept of Computer Engg, Cankaya, Ankara, Turkey

    Murat Manguoğlu

  3. Middle East Technical University Mathematics & Institute of Applied Mathe, Ankara, Turkey

    Münevver Tezer-Sezgin

  4. Civil Engineering & Applied Mathematics, Middle East Technical University, Ankara, Turkey

    Serdar Göktepe

  5. Institute of Applied Mathematics, Middle East Technical University Institute of Applied Mathematics, Ankara, Turkey

    Ömür Uğur

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Ohlberger, M., Rave, S., Schindler, F. (2016). Model Reduction for Multiscale Lithium-Ion Battery Simulation. In: Karasözen, B., Manguoğlu, M., Tezer-Sezgin, M., Göktepe, S., Uğur, Ö. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2015. Lecture Notes in Computational Science and Engineering, vol 112. Springer, Cham. https://doi.org/10.1007/978-3-319-39929-4_31

Download citation

Publish with us

Policies and ethics

Search

Navigation