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Derivation of a Local Volume-Averaged Model and a Stable Numerical Algorithm for Multi-Dimensional Simulations of Conversion Batteries

In this article, we derive a general form of local volume-averaging theory and apply it to a model of zinc-air conversion batteries. Volume-averaging techniques are frequently used for the macroscopic description of micro-porous electrodes. We extend the existing method by including reactions between different phases and time-dependent volume fractions of the solid phases as these are continuously dissolved and reconstructed during operation of conversion batteries. We find that the constraint of incompressibility for multi-component fluids causes numerical instabilities in simulations of zinc-air battery cells. Therefore, we develop a stable sequential semi-implicit algorithm which converges against the fully implicit solution. Our method reduces the coupling of the variables by splitting the system of equations and introducing an additional iteration step.