Verification and Validation of a Coordinate Transformation Method in Axisymmetric Transient Magnetics.

We present a verification and validation analysis of a coordinate-transformation-based numerical solution method for the two-dimensional axisymmetric magnetic diffusion equation, implemented in the finite-element simulation code ALEGRA. The transformation, suggested by Melissen and Simkin, yields an equation set perfectly suited for linear finite elements and for problems with large jumps in material conductivity near the axis. The verification analysis examines transient magnetic diffusion in a rod or wire in a very low conductivity background by first deriving an approximate analytic solution using perturbation theory. This approach for generating a reference solution is shown to be not fully satisfactory. A specialized approach for manufacturing an exact solution is then used to demonstrate second-order convergence under spatial refinement and temporal refinement. For this new implementation, a significant improvement relative to previously available formulations is observed. Benefits in accuracy for computed current density and Joule heating are also demonstrated. The validation analysis examines the circuit-driven explosion of a copper wire using resistive magnetohydrodynamics modeling, in comparison to experimental tests. The new implementation matches the accuracy of the existing formulation, with both formulations capturing the experimental burst time and action to within approximately 2%.