High-voltage DC relays are widely used in electric vehicles. Due to the presence of capacitive elements in the circuit, a large inrush current occurs at the moment of power-on, resulting in arcing between the relay contacts. This process erodes the contact surfaces, adversely affecting the relay's performance and lifespan. Although improvements such as pre-charged circuits are available, capacitive power-on arc erosion remains common. Therefore, this paper presents a two-dimensional simulation model for high-voltage DC relays, based on magnetohydrodynamics. The model incorporates two arc extinguishing methods: high-voltage arc extinguishing medium and magnetic blowout arc extinction. The simulation model is used to examine the dynamic process of arc erosion and the extent of contact erosion. Subsequently, the study selected eight operating conditions for simulations and experiments, then conducted a correlation analysis between the areas of contact melt pools post-simulation and the areas of contact erosion post-experiment. This confirmed the consistency of trends between the simulation results and experimental outcomes. Based on this, the study analyzes the effects of voltage, current, and capacitance on arc erosion, summarizing the physical processes and principles of arc erosion under different factors, and further examines the mechanisms of these factors from perspectives such as maximum instantaneous power and arc energy. Finally, the results indicate that current has the most significant impact on contact arc erosion. The simulation model has broad applicability and provides practical significance for analyzing arc erosion under capacitive inrush currents in high-voltage DC relays, significantly improving research efficiency.