We are interested in simulating a variety of problems in 3 dimensions (3D) featuring large electric currents. While 2D simulations have been quite informative, cylindrical symmetry may interfere with a problem’s relevant physics. Specifically, all objects in the domain behave as if they are extruded 360°—turning particles into hoops. In dealing with electrical current, this can have serious ramifications on the current pathways. In 3D (r, φ, z) currents can adjust their pathways anywhere along those 360 degrees given the right conditions; however, in 2D (r, z) those pathways can be completely choked off because an insulating hoop, rather than a particle, is present.
2016 IEEE/ACES International Conference on Wireless Information Technology, ICWITS 2016 and System and Applied Computational Electromagnetics, ACES 2016 - Proceedings
We explore how reliable the ALEGRA MHD code is in its static limit. Also, we explore (in the quasi-static approximation) the process of evolution of the magnetic fields inside and outside an inclusion and the parameters for which the quasi-static approach provides for self-consistent results.
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 tem- poral 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%.
Weak scaling studies were performed for the explicit solid dynamics component of the ALEGRA code on two Cray supercomputer platforms during the period 2012-2015, involving a production-oriented hypervelocity impact problem. Results from these studies are presented, with analysis of the performance, scaling, and throughput of the code on these machines. The analysis demonstrates logarithmic scaling of the average CPU time per cycle up to core counts on the order of 10,000. At higher core counts, variable performance is observed, with significant upward excursions in compute time from the logarithmic trend. However, for core counts less than 10,000, the results show a 3 × improvement in simulation throughput, and a 2 × improvement in logarithmic scaling. This improvement is linked to improved memory performance on the Cray platforms, and to significant improvements made over this period to the data layout used by ALEGRA.
The finite-element shock hydrodynamics code ALEGRA has recently been upgraded to include an X-FEM implementation in 2D for simulating impact, sliding, and release between materials in the Eulerian frame. For validation testing purposes, the problem of long-rod penetration in semi-infinite targets is considered in this report, at velocities of 500 to 3000 m/s. We describe testing simulations done using ALEGRA with and without the X-FEM capability, in order to verify its adequacy by showing X-FEM recovers the good results found with the standard ALEGRA formulation. The X-FEM results for depth of penetration differ from previously measured experimental data by less than 2%, and from the standard formulation results by less than 1%. They converge monotonically under mesh refinement at first order. Sensitivities to domain size and rear boundary condition are investigated and shown to be small. Aside from some simulation stability issues, X-FEM is found to produce good results for this classical impact and penetration problem.