Numerical modeling of the velocity skin effects: An investigation of issues affecting accuracy

This paper explores the factors that affect the accuracy of numerical analy sis of railguns with motion using Electromechanical Analysis Program in Thr ee Dimensions (EMAP3D) [1], a Lagrangian finite element method (FEM) code t hat models thermal and electromagnetic diffusion into conductors with molin g interfaces. In situations involving sliding electric contact between cond uctors, EMAP3D solves a series of velocity-dependent diffusion problems in which the armature moves to different axial positions that satisfy the equa tions of motion for the armature, This paper develops two relationships bet ween time step size and solution accuracy. One relationship is a lon-er bou nd on time step size, based on the need for linear brick elements to repres ent 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 poi nt accurate solutions to problems involving motion are no longer possible f or given mesh dimensions. The velocity at which accurate solutions are poss ible can be increased by increasing the resolution of the mesh. At present, a practical limit to simulating realistic railgun problems is less than 50 0 m/s, Because this limit is set by rapidly advancing state-of-the-art comp uter hardware, the prospects for achieving higher velocities in the near fu ture are good.