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A high-fidelity arc plasma simulation tool has been developed that can model arc physics coupled with electrode erosion. The arc physics is modelled using an equilibrium, resistive magneto-hydrodynamic (MHD) model. Solid electrodes are modelled using an immersed boundary method that allows for the electrodes to deform dynamically without modifying the original mesh or the underlying governing equations. First, a partial validation of the arc physics is performed by comparing arc stretch in cross-flow with experimental results across a 1.1 mm spark gap. Subsequently, the ability to model arc physics in a coupled manner with ablating electrodes is demonstrated in 2D using a 0.7 mm electrode gap with iron electrodes. The objective of this work is to illustrate modeling of coupled arc physics with eroding electrodes; a capability that will be extended for the realistic prediction of spark plug lifetimes in future work.