Abstract
In order to achieve a better understanding of degradation processes in lithium-ion batteries, the modelling of cell dynamics at the mircometer scale is an important focus of current mathematical research. These models lead to large-dimensional, highly nonlinear finite volume discretizations which, due to their complexity, cannot be solved at cell scale on current hardware. Model order reduction strategies are therefore necessary to reduce the computational complexity while retaining the features of the model. The application of such strategies to specialized high performance solvers asks for new software designs allowing flexible control of the solvers by the reduction algorithms. In this contribution we discuss the reduction of microscale battery models with the reduced basis method and report on our new software approach on integrating the model order reduction software pyMOR with third-party solvers. Finally, we present numerical results for the reduction of a 3D microscale battery model with porous electrode geometry.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
pyMOR—Model Order Reduction with Python. http://www.pymor.org
Bastian, P., Blatt, M., Dedner, A., Engwer, C., Klöfkorn, R., Ohlberger, M., Sander, O.: A generic grid interface for parallel and adaptive scientific computing. Part I: abstract framework. Computing 82(2–3), 103–119 (2008)
Drohmann, M., Haasdonk, B., Kaulmann, S., Ohlberger, M.: A software framework for reduced basis methods using Dune-RB and RBmatlab. In: Dedner, A., Flemisch, B., Klöfkorn, R. (eds.) Advances in DUNE, pp. 77–88. Springer, Berlin Heidelberg (2012)
Drohmann, M., Haasdonk, B., Ohlberger, M.: Reduced basis approximation for nonlinear parametrized evolution equations based on empirical operator interpolation. SIAM J. Sci. Comput. 34(2), A937–A969 (2012)
Haasdonk, B., Ohlberger, M.: Reduced basis method for finite volume approximations of parametrized linear evolution equations. m2an. Math. Model. Numer. Anal. 42(2), 277–302 (2008)
Iliev, O., Latz, A., Zausch, J., Zhang, S.: On some model reduction approaches for simulations of processes in Li-ion battery. In: Proceedings of Algoritmy 2012, Conference on Scientific Computing, Vysoké Tatry, Podbanské, Slovakia, pp. 161–171. Slovak University of Technology in Bratislava (2012)
Latz, A., Zausch, J.: Thermodynamic consistent transport theory of li-ion batteries. J. Power Sources 196(6), 3296–3302 (2011)
Less, G.B., Seo, J.H., Han, S., Sastry, A.M., zausch, J., latz, A., schmidt, S., wieser, C., kehrwald, D., fell, S.: Micro-scale modeling of li-ion batteries: parameterization and validation. J. Electrochem. Soc. 159(6), A697 (2012)
Popov, P., Vutov, Y., Margenov, S., Iliev, O.: Finite volume discretization of equations describing nonlinear diffusion in li-ion batteries. In: Dimov, I., Dimova, S., Kolkovska, N. (eds.) Numerical Methods and Applications. Lecture Notes in Computer Science, vol. 6046, pp. 338–346. Springer, Berlin Heidelberg (2011)
Acknowledgments
This work has been supported by the German Federal Ministry of Education and Research (BMBF) under contract number 05M13PMA.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Ohlberger, M., Rave, S., Schmidt, S., Zhang, S. (2014). A Model Reduction Framework for Efficient Simulation of Li-Ion Batteries. In: Fuhrmann, J., Ohlberger, M., Rohde, C. (eds) Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems. Springer Proceedings in Mathematics & Statistics, vol 78. Springer, Cham. https://doi.org/10.1007/978-3-319-05591-6_69
Download citation
DOI: https://doi.org/10.1007/978-3-319-05591-6_69
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-05590-9
Online ISBN: 978-3-319-05591-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)