# Modeling discontinuous potential distributions using the finite volume method, and application to liquid metal batteries

## TL;DR

This paper introduces a finite volume method-based model for simulating three-dimensional electrical potential distributions in batteries with internal voltage jumps, validated on a liquid metal battery system.

## Contribution

It develops a novel finite volume discretization that accurately captures internal voltage jumps at electrode-electrolyte interfaces in battery models.

## Key findings

- Successfully validated with analytical test case
- Simulated current distribution in a Li||Bi liquid metal battery
- Analyzed discharge curve behavior

## Abstract

The electrical potential in a battery jumps at each electrode-electrolyte interface. We present a model for computing three-dimensional current and potential distributions, which accounts for such internal voltage jumps. Within the framework of the finite volume method we discretize the Laplace and gradient operators such that they account for internal jump boundary conditions. After implementing a simple battery model in OpenFOAM we validate it using an analytical test case, and show its capabilities by simulating the current distribution and discharge curve of a Li||Bi liquid metal battery.