A Lagrangian Approach to the Simulation of a Constricted Vacuum Arc in a Magnetic Field

The use of numerical simulations of vacuum arcs can be very useful in order to improve the performance of vacuum interrupters. Standard computational fluid dynamics methods based on the Eulerian approach have difficulties to deal with this kind of problem, so a new technique is proposed, based on a Lagrangian approach. In order to focus on the performance of the new approach and not on specific details of a full model, a simplified arc model is used to investigate the capabilities of a Lagrangian approach in the context of vacuum arc simulations. The focus of this initial study is on implementing the necessary ingredients, that is, the development of a compressible flow solver, the introduction of the relevant boundary conditions and the coupling with the current conservation equation for the electric current. In addition, the stability of such a numerical scheme is evaluated. Furthermore, comparisons with results obtained using commercial software are also provided to demonstrate the validity of the results obtained with the new methodology.