A Darwin Time Domain Scheme for the Simulation of Transient Quasistatic Electromagnetic Fields Including Resistive, Capacitive and Inductive Effects
A Darwin Time Domain Scheme for the Simulation of Transient Quasistatic Electromagnetic Fields Including Resistive, Capacitive and Inductive Effects
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用于模拟瞬态准静态电磁场（包括电阻、电容和电感效应）的达尔文时域方案
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
S. Schöps
中科院分区：
文献类型：
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作者：
M. Clemens;B. Kähne;S. Schöps
达尔文场模型解决了麦克斯韦方程组的近似问题，其中忽略了辐射效应。它可以描述一般的准静态电磁场现象，包括电感、电阻和电容效应。基于达尔文-安培方程和隐式包含的达尔文连续性方程的达尔文公式产生了通过应用几何空间离散化方案和隐式向后微分时间积分方法而获得的非对称且病态的代数方程组。提出了一个两步解决方案，其中底层的块高斯-赛德尔方法被证明可以改变最初选择的规范条件，并且所得方案仅需要在每个时间步中连续求解弱耦合电准静态和磁准静态离散场公式。数值测试问题的结果验证了所选择的方法。
The Darwin field model addresses an approximation to Maxwell's equations where radiation effects are neglected. It allows to describe general quasistatic electromagnetic field phenomena including inductive, resistive and capacitive effects. A Darwin formulation based on the Darwin-Ampere equation and the implicitly included Darwin-continuity equation yields a non-symmetric and ill-conditioned algebraic systems of equations received from applying a geometric spatial discretization scheme and the implicit backward differentiation time integration method. A two-step solution scheme is presented where the underlying block-Gauss-Seidel method is shown to change the initially chosen gauge condition and the resulting scheme only requires to solve a weakly coupled electro-quasistatic and a magneto-quasistatic discrete field formulation consecutively in each time step. Results of numerical test problems validate the chosen approach.