A Lagrangian formulation for mechanically, thermally coupled electromagnetic diffusive processes with moving conductors

In a moving physical system, field variables can be described by functions of time and initial (reference) positions of particles (Lagrangian description) or functions of time and current positions of particles (Eulerian description). Lagrangian formulation exhibits several advantages in modeling electromagnetic (EM) diffusion problems with moving conductors. It results in a symmetric coefficient matrix which reduces computational cost and central memory requirement. It also eliminates numerical instability at hypervelocity. In the simulation of EM launchers, Lagrangian formulation facilitates EM analyses including end (breech and muzzle) effects, and the effects of imperfect rails and structural deformation. A detailed Lagrangian formulation of mechanically, and thermally coupled electromagnetic diffusive processes with moving conductors is presented in this paper. It is based on the quasistatic Maxwell´s equations in terms of dual potentials: magnetic vector potential and electric scalar potential. With the Coulomb gauge condition, magnetic vector potential is uniquely determined. The formulation has been implemented in the finite element program ´EMAP3D´ (Electro-Mechanical Analysis Program in 3 Dimension). The thermally coupled electromagnetic simulation of a railgun is illustrated. The distributions of current density, magnetic field, and temperature are presented. Also the profiles of velocity and current are shown.<>