An MPMD approach coupling electromagnetic continuum mechanics approximations in ALEGRA

• Published in: Computer methods in applied mechanics and engineering Vol. 429; p. 117164
• Main Authors: Robinson, Allen C., Drake, Richard R., Luchini, Christopher B., Moral, Ramón J., Niederhaus, John H.J., Petney, Sharon V.
• Format: Journal Article
• Language: English
• Published: United States Elsevier B.V 01-09-2024; Elsevier
• Subjects: Asymptotic; Circuit; Computing; Electromagnetics; Electromechanics; ENGINEERING; Magnetohydrodynamics; Modeling; MPMD; Multiple data; Multiple program; Parallel; Electromechanics; Magnetohydrodynamics; Multiple program; Asymptotic; Multiple data; Circuit; Parallel; Computing; Modeling; Electromagnetics; MPMD
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2024.117164

Two complementary approximations for describing aspects of continuum electromagnetics in moving media are discussed: electroquasistatic and magnetoquasistatic. Each has been implemented in the finite element shock code ALEGRA for modeling dynamic electromechanical phenomena on typical engineering time scales, with fully integrated circuit coupling (Niederhaus et al. 2023). The approximations can be obtained by consistent asymptotic balancing of Maxwell’s equations relative to timescales associated with magnetic diffusion, charge relaxation, and electromagnetic wave propagation. In ALEGRA, the electroquasistatic approximation is used for ferroelectric (FE) modeling, while the magnetoquasistatic approximation is used for magnetohydrodynamic (MHD) modeling. In this paper we introduce for the first time a detailed derivation of a useful quasi-steady “low-Rm” variant of the MHD approximation applicable for cases, such as with detonators, where the thermodynamic pressure arising from Joule heating dominates over magnetic forces. An additional purpose of this paper is to present a coupling mode using Multiple Program-Multiple Data (MPMD) message passing communication that allows the user to run 3D FE problems together with 2D and/or 3D MHD problems with the respective simulation domains coupled through a common circuit equation. The MPMD coupling capability is used here to model the dynamic coupling of a notional ferroelectric generator with an RP-87 exploding bridgewire detonator. The simulated bridgewire heats up and bursts under current generated by simulated depoling of the ferroelectric generator, as a demonstration of the MPMD capability.
•We survey three models coupling solid dynamics with the equations of Maxwell.•We derive a simplified MHD model for cases where Joule energy deposition dominates.•MPMD computing couples finite element simulations via an electrical circuit model.•A bridgewire detonator model driven by a ferroelectric generator model is created.