Department of Experimental Audiology, Otto von Guericke University Magdeburg, Leipziger Straße 44, 39120 Magdeburg, Germany.
Phys Rev E. 2017 Dec;96(6-1):063306. doi: 10.1103/PhysRevE.96.063306. Epub 2017 Dec 13.
The present work shows a method for stable simulations via the lattice Boltzmann (LB) model for electromagnetic waves (EM) transiting homogeneous media. LB models for such media were already presented in the literature, but they suffer from numerical instability when the media transitions are sharp. We use one of these models in the limit of pure vacuum derived from Liu and Yan [Appl. Math.
38, 1710 (2014)AMMODL0307-904X10.1016/j.apm.2013.09.009] and apply an extension that treats the effects of polarization and magnetization separately. We show simulations of simple examples in which EM waves travel into media to quantify error scaling, stability, accuracy, and time scaling. For conductive media, we use the Strang splitting and check the simulations accuracy at the example of the skin effect. Like pure EM propagation, the error for the static limits, which are constructed with a current density added in a first-order scheme, can be less than 1%. The presented method is an easily implemented alternative for the stabilization of simulation for EM waves propagating in spatially complex structured media properties and arbitrary transitions.
本工作展示了一种通过晶格玻尔兹曼（LB）模型对电磁波（EM）穿过均匀介质进行稳定模拟的方法。LB 模型已经在文献中提出用于此类介质，但当介质过渡尖锐时，它们会受到数值不稳定性的影响。我们在刘和严的纯真空极限中使用其中一个模型[应用数学模型，38，1710（2014）AMMODL0307-904X10.1016/j.apm.2013.09.009]，并应用一种扩展方法，分别处理极化和磁化的影响。我们展示了一些简单示例的模拟，以量化误差缩放、稳定性、准确性和时间缩放。对于导电介质，我们使用 Strang 分裂，并在皮肤效应的示例中检查模拟的准确性。与纯 EM 传播一样，由一阶方案中添加电流密度构建的静态极限的误差可以小于 1%。所提出的方法是一种易于实现的替代方案，可用于稳定模拟在空间复杂结构介质特性和任意过渡中传播的 EM 波。
