Numerical modeling of the velocity skin effects: an investigation of issues affecting accuracy [in railguns]

This paper explores the factors that affect the accuracy of numerical analysis of railguns with motion using Electromechanical Analysis Program in Three Dimensions (EMAP3D), a Lagrangian finite element method (FEM) code that models thermal and electromagnetic diffusion into conductors with moving interfaces. In situations involving sliding electric contact between conductors, EMAP3D solves a series of velocity-dependent diffusion problems in which the armature moves to different axial positions that satisfy the equations of motion far the armature. This paper develops two relationships between time step size and solution accuracy. One relationship is a lower bound on time step size, based on the need for linear brick elements to represent accurately the exponential-like spatial variation of current density as currents diffuse into conductors. The other relationship is an upper bound, which limits the motion of the armature to distances on the scale of the current distribution around the armature. Because the upper bound decreases with increasing velocity, the two bounds eventually converge, at which point accurate solutions to problems involving motion are no longer possible for given mesh dimensions. The velocity at which accurate solutions are possible can be increased by increasing the resolution of the mesh. At present, a practical limit to simulating realistic railgun problems is less than 500 m/s. Because this limit is set by rapidly advancing state-of-the-art computer hardware, the prospects for achieving higher velocities in the near future are good.