| Summary: | 碩士 === 國立中正大學 === 機械工程學系暨研究所 === 101 === Based on the Bérenger’s concept of perfectly matched layer (PML) absorbing boundary in the finite-difference time-domain (FDTD) method, this study proposes a lattice Boltzmann (LB) scheme that incorporates the PML technique for to simulating propagating electromagnetic waves in a two-dimensional medium. By introducing additional layers at boundary for reduction the reflection of electromagnetic waves, the PML effect is managed as a forcing term and incorporated into the LB evolution equations. The consistence between the proposed LB scheme and the macroscopic PML expressions is demonstrated using the technique of the Chapman-Enskog multi-scale analysis. Compared with the general LB method, the PML-LBM method has superior lattice absorption for the case of radiation boundary. When an eight PML boundary layers of the parabolic absorption function was used, the reflectivity could be reduced to 0.036%. This method does not only satisfy energy conservation, but also maintain a second order accuracy spatially. For performing both simulation cases of a simple transmission of an electromagnetic wave and the interactions of electric dipoles, the computational time of the PML-LBM is shorter than that of the PML-FDTD. For a 400 400 lattices with 20 PML boundary layers, the computation time for the PML-LBM is 46.38% shorter than that of for the PML-FDTD. The present PML-LBM scheme is based on the D2Q5 lattice, the limited discrete velocities, however, restricts its capability in reflection absorption. Results show that, under the same number of PML layers, the PML-FDTD demonstrations better ability in reflection absorption.
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