Hauser A, Verhey J L
Department of Experimental Audiology, Otto von Guericke University Magdeburg, Leipziger Straße 44, 39120 Magdeburg, Germany.
Phys Rev E. 2019 Mar;99(3-1):033301. doi: 10.1103/PhysRevE.99.033301.
A three-dimensional lattice-Boltzmann model (LBM) for the simulation of the Maxwell equations is presented. The inclusion of media follows an extension of a special limit described in the literature which is applicable to this LBM and does not harm the stability of simulations. The focus of the present study lies on the properties of numerical accuracy and stability of the LBM in comparison to the standard finite-difference time-domain (FDTD) method based on Yee's method. Typical examples, often investigated in the context of numerical simulations, are considered. These include the propagation of electrodynamic (EM) fields in one- and three-dimensional systems. Results of this simulations are compared to the ones of their theoretical predictions. Further on, long-time simulations are done in systems with periodic boundary conditions to check if the total energy is conserved. To investigate the effect of the numeric impedance, the propagation of an EM pulse is monitored spatially and temporarily in a two-dimensional system. The simulation results indicate, in contrast to the one obtained from the FDTD method, that the presented LBM does fulfill the expected energy conservation and is not effected by the numerical impedance. This LBM therefore represents a valuable alternative for the simulation of EM problems like long-time simulations by avoiding intrinsic properties the FDTD method suffers from.
