Magnetic field based finite element method for magneto-static problems with discontinuous electric potential distributions

We introduce two finite element formulations to approximate magneto-static problems with discontinuous electric potential based respectively on the electrical scalar potential and the magnetic field. This work is motivated by our interest in Liquid Metal Batteries (LMBs), a promising technology for storing intermittent renewable sources of energy in large scale energy storage devices. LMBs consist of three liquid layers stably stratified and immiscible, with a light liquid metal on top (negative electrode), a molten salt in the middle (electrolyte) and a heavier liquid metal on bottom (positive electrode). Energy is stored in electrical potential differences that can be modeled as jumps at each electrode-electrolyte interface. This paper focuses on introducing new finite element methods for computing current and potential distributions, which account for internal voltage jumps in liquid metal batteries. Two different formulations that use as primary unknowns the electrical potential and magnetic field, respectively, are presented. We validate them using various manufactured test cases, and discuss their applications for simulating the current distribution during the discharge phase in a liquid metal battery.