COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering For Authors The reduced basis method applied to transport equations of a lithium-ion battery

Abstract

The reduced basis method applied to transport equations of a lithium-ion battery Stefan Volkwein Andrea Wesche Article information: To cite this document: Stefan Volkwein Andrea Wesche , (2013),"The reduced basis method applied to transport equations of a lithium-ion battery" If you would like to write for this, or any other Emerald publication, then please use our Emerald for Authors service information about how to choose which publication to write for and submission guidelines are available for all. Please visit www.emeraldinsight.com/authors for more information. About Emerald www.emeraldinsight.com Emerald is a global publisher linking research and practice to the benefit of society. The company manages a portfolio of more than 290 journals and over 2,350 books and book series volumes, as well as providing an extensive range of online products and additional customer resources and services. Abstract Purpose – In this paper, the authors aim to show how to apply the reduced basis method to the transport equations of a lithium-ion battery. Design/methodology/approach – The authors consider a coupled system of nonlinear parameterized partial differential equations (P 2 DEs), which models the concentrations and the potentials in lithium-ion batteries. Findings – The authors develop an efficient reduced basis approach for the fast and robust numerical solution of the P 2 DE system. Originality/value – By the reduced basis method, the authors get (reduced) solutions with a speed up factor of up to 18 in the presented examples in comparison to the original finite volume solutions. I. Introduction The modelling of lithium-ion batteries has received an increasing amount of attention in the recent past. Several companies worldwide are developing such batteries for consumer electronic applications, in particular, for electric-vehicle applications. To achieve the performance and lifetime demands in this area, exact mathematical models of the battery are required. Moreover, the multiple evaluation of the battery model for different parameter settings involves a large amount of time and experimental effort. Here, the derivation of reliable mathematical models and their efficient numerical realization are very important issues in order to reduce both time and cost in the improvement of the performance of batteries. In the present work we consider a mathematical model for lithium-ion batteries which describes the transport processes by a partial differential equation system. This model is developed in the paper by Popov et al. (2010). The physical and chemical