Fast algorithm for calculating the surface concentration of spherical particles for lithium-ion battery simulations

For modelling the porosity of the electrodes in a lithium-ion battery the electrode materials are described by spherical particles. With these particles the main chemical reaction, the diffusion of lithium into the electrodes, is described. Because the main reaction occurs at the surface of a particle a numerically efficient solver which is able to predict the correct surface concentration with only a few discretization points in the bulk is developed. The new algorithm is compared to a standard finite difference scheme with respect to accuracy, the number of discretization points used, and calculation time.