A mixed finite element spatial discretization scheme and a higher-order accurate temporal discretization scheme for a strongly discontinuous electromagnetic interface condition in ideal sliding electrical contact problems

Sliding electrical contact involves multiple conductors sliding in contact at different speeds, with current flowing through the contact surfaces. The Lagrangian method is commonly used to describe the electromagnetic field in order to overcome the trouble of convective dominance, especially in high-speed sliding electrical contact problems. However, to maintain correct field continuity, magnetic vector potential $A^{\prime }$ and scalar potential ${\varphi }^{\prime }$ taken as variables cannot be continuous simultaneously at the ideal sliding electrical contact interface. This involves a strongly discontinuous condition for variables. Further, commonly used spatial–temporal discretization algorithms are invalid, for example, the classic finite element (CFEM) framework does not allow discontinuous variables, and the backward Euler method in time domain introduces a significant interface error source associated with the velocity of relative motion. To accurately handle strongly discontinuous conditions in numerical calculations, a mixed nodal finite element scheme and a higher-order accurate temporal discretization scheme are introduced. In this scheme, classical finite element method is performed in each subdomain, and the derivative terms at the boundary are added as new variables. The effectiveness and accuracy of the above methods are verified by comparing them with a standard solution in a two-dimensional railgun model and analyzing the current density distribution in a three-dimensional railgun model.