The Study Of Lattice Boltzmann Method For Electromagnetic Waves

Lattice Boltzmann method (LBM) is a numerical method for fluid flow andcomplex system which arises in the end of last century. It has some advantages thatbring much attention, such as their algorithmic simplicity, parallel computation, easyhandling of complex boundary conditions, and efficient numerical simulations. Thismethod has been widely used to the nonlinear partial differential equation in recentyears. In this paper, we employ the lattice Boltzmann method to investigate theMaxwell equations, as follows:First, we reviewed the history and current research of the lattice Boltzmannmethod.Second, we solve the Maxwell equations with the lattice Boltzmann method,and propose the lattice Boltzmann model for the Maxwell vorticity equations withthree order truncation error. At the same time, we give the expression of distributionfunction and the stability conditions.Third, numerical experiments are done with the models in Chapter2, someclassical examples are simulated, including the electric field and equipotential linesaround an electrostatic dipole, and the electric and magnetic fields around anoscillating dipole etc.. some classical are simulated, including the interference of twopoint sources, diffraction, reflection, refraction etc.. We compared numerical results ofthe lattice Boltzmann models to solutions getting other methods. The results show thisthree order model can be used to simulate the Maxwell equations, and this model has three order accuracy.Finally, we gives the conclusion and deals with the major conclusions of thepresent study.