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-” 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.

中文翻译：

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ALEGRA 中耦合电磁连续介质力学近似的 MPMD 方法


讨论了描述移动介质中连续电磁学方面的两个互补近似：电准静态和磁准静态。每个都已在有限元冲击代码 ALEGRA 中实现，用于在典型工程时间尺度上对动态机电现象进行建模，并具有完全集成电路耦合（Niederhaus 等人，2023）。这些近似值可以通过麦克斯韦方程相对于磁扩散、电荷弛豫和电磁波传播相关的时间尺度的一致渐近平衡来获得。在 ALEGRA 中，电准静态近似用于铁电 (FE) 建模，而磁准静态近似用于磁流体动力学 (MHD) 建模。在本文中，我们首次介绍了 MHD 近似的有用准稳态“低”变体的详细推导，该变体适用于雷管等情况，其中焦耳热产生的热力学压力比磁力占主导地位。本文的另一个目的是提出一种使用多程序多数据 (MPMD) 消息传递通信的耦合模式，该模式允许用户将 3D FE 问题与 2D 和/或 3D MHD 问题一起运行，并通过常见的电路方程。此处使用 MPMD 耦合功能对概念铁电发电机与 RP-87 爆炸桥线雷管的动态耦合进行建模。模拟桥线在铁电发电机模拟去极化产生的电流下升温并破裂，作为 MPMD 能力的演示。