Extremely Fast Solvers for Newman-Type Models of Li-Ion Cell (dis)Charge

Abstract

The Newman model for charge transport within porous electrodes was developed by Newman, Fuller and Doyle in the mid-90s, and has become the standard tool for simulating Li-ion cell (dis)charge. The model is comprised of a system of nonlinear partial differential equations that must, in general, be solved numerically.The computational costs associated with solving the Newman model, even for a single planar cell, are relatively high; for example, most solvers take several minutes to compute a single discharge curve. This makes its application to computationally expensive problems (such as cell optimisation, parameter estimation or battery pack simulation) problematic. Motivated by the lack of a fast Newman solver in the literature we have developed a new software tool, named DandeLiion. This provides extremely fast code with which to solve the Newman model. It is straightforward to install, comes with concise and clear documentation, is fully parallelisable and free to use. As an example of its power it has the capability of simulating a full discharge curve in less than a second (with fully nonlinear transport and sufficient resolution to compute the solution to several digits of accuracy) which is approximately several hundred times faster than most commercial solvers. In addition, it is equipped with a library of battery chemistries that incorporates models for nonlinear lithium transport and open circuit voltage in most active electrode materials, and for lithium transport and conduction in the most common electrolytes. This gives the user the ability to simulate a wide range of devices designs. It can also be used to simulate realistic drive cycle data.In order to illustrate the power of this software we perform a thermally coupled simulation in a realistic pouch cell geometry, using DandeLiion to compute the electrochemical discharge of the cell stack in the resulting three-dimensional evolving temperature field. We note that such thermally coupled pack simulations are normally performed using simple equivalent circuit models of the cell, rather than the Newman model, because the computational cost associated with a thermally heterogenous Newman model has, up until now, been too high.