ALEGRA-MHD Simulations for Magnetization of an Ellipsoidal Inclusion

Report No. ARL-TR-8092
Authors: Michael Grinfeld; John Niederhaus
Date/Pages: August 2017; 26 pages
Abstract: Here we verify how reliable the ALEGRA MHD code is in its static limit. We explore in the quasi-static approximation the process of evolution of the magnetic fields inside and outside an inclusion. A simple closed-form analytic solution similar to the Eshelby theory is derived for magnetic induction in an ellipsoidal inclusion of magnetically permeable material after magnetic diffusion has saturated. The simplicity of the interior solution lends itself well to verification of computational electromagnetic simulations. Convergence testing under spatial mesh refinement using this exact solution shows that the equilibrium magnetized state can be reached by transient means via computation with ALEGRA. The computed solution in the interior core of the ellipsoid converges to the exact solution at first order, as expected, for a very large range of spatial mesh sizes spanning the very coarsest to the very finest meshes that can be used. The error in the computed solution is dominated by the interfacial region where mixed-material elements are present. When the interfacial region is included, the error magnitudes are larger by more than an order of magnitude, and the convergence rate drops from roughly 1 to roughly 0.5. These issues appear to be associated with the enforcement of natural interface conditions and the element-level homogenization scheme for mixed-material elements.
Distribution: Approved for public release
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Last Update / Reviewed: August 1, 2017