Model Reduction for Multiscale Lithium-Ion Battery Simulation
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.
KeywordsProper Orthogonal Decomposition Model Reduction Current Collector Porous Electrode Proper Orthogonal Decomposition Mode
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.
- 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
- 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
- 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
- 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”, SIAMGoogle 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. 161–171zbMATHGoogle 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. 421–429Google 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. 695–702Google 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. 338–346Google 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+2Google Scholar
- 30.V. Taralova, Upscaling approaches for nonlinear processes in lithium-ion batteries, Ph.D. thesis, Kaiserslautern, Technische Universität Kaiserslautern, 2015, pp. VII, 224Google Scholar