Nitsche Mortar Finite Element Method for Electromagnetic Field Numerical Calculations With Nonmatching Meshes in Railguns

The railgun’s armature and rail are in high-speed sliding electrical contact, and there is a velocity skin effect regarding electromagnetic field distribution. Under this effect, current density is locally concentrated and is complex near the armature-rail interface. To ensure accuracy, mesh sizes need to be sufficiently fine around the armature-rail interface and the rail’s surface. Meanwhile, the Lagrangian method is commonly used to describe electromagnetic fields involving moving conductors, requiring a nearly structured mesh shape. Given the constraint of the mesh shape, implementing a meshing method that allows for appropriate and flexible mesh sizes is challenging, which may lead to inefficient and low-accuracy simulations. In this article, an efficient nonmatching meshing method is introduced to deliver structured meshes with appropriate and flexible sizes. Furthermore, the Nitsche mortar finite element method is used to ensure the continuity conditions across nonmatching interfaces in a weak sense. This method incorporates additional boundary integral terms into variational formulas. Current density results obtained using matching and nonmatching meshes were compared at velocities of 30 and 100 m/s, proving the correctness and efficiency of the nonmatching meshing method. In addition, current density distribution using nonmatching meshes was analyzed at velocities of 100, 500, and 1000 m/s, further demonstrating the feasibility of the abovementioned methods.