A Lattice Boltzmann Model For Maxwell Equations

Maxwell's equations were created by a British physicist scientist named Maxwell in order to describe the electromagnetism field. The equations describe the electric field and magnetic field respectively, and also describe the relation between them. In the Maxwell equations, electric field and magnetic field are described as an in divisible macrocosm, thus completely generalized the basic regulation of electromagnetism field, at the same time, and predicted the existence of electromagnetic wave.The classic "field theory" born after 19th century was established by Maxwell after his summing up the three experiment laws of electromagnetism and combined it with the type of mechanics model. The main merit of Maxwell is that he can jump of the classic mechanics frame, and during the study of physics he paid attention to the "field" instead of "mechanic".This led him to go into differ from the vector of classic mathematics to be partial to a differential calculus operation sign while using the mathematics tool. All of the Maxwell's works are the foundations that make him discover the electromagnetic wave equation. It is thus clear that, actually Maxwell has already broken through the frame of classic mathematics and classic physics, but limited by the science level at that time, people still only can comprehend the electromagnetism from the frame of classic mathematics and mechanics.The lattice Boltzmann methods (LBM) has attracted lots of experts on fluid mechanics field as an alternative calculation of fluid mechanics. Discriminate between those former methods based on macroscopic continuous equation; the LBM takes the mesoscopic kinetic equation as a starting point. So far, the LBM has already developed to imitate parts of the nonlinear partial differential equations, for example, Burgers equation, Sine-Gordon equation, KdV equation, etc.Under the general circumstance, the space, time, speed are separate on one blank. After choosing the appropriate equilibrium distribution function, we expand the distribution function to the third order by Chapman-Enskog expansion and use the conservation law in time scale to to analysis the macroscopic physical equation. From the emergence of electromagnetism theory to now, the academic circles have always been using the classic mathematics of the Europe surname space as tool to solve the Maxwell equations. This text adopts the lattice Boltzmann methods which are different from the traditional classic mathematics methods to solve the Maxwell equations.The text commences regularization of the Maxwell equation. Firstly, dissolve the Maxwell equations to the form of tensor.Then according to the request of lattice Boltzmann methods, import two appropriate equilibrium distribution function for electric field and magnetic field. Through processing the frontal two of the series lattice Boltzmann equations, we will get the 2-stratum Maxwell equation. Last, we need to deal with the high-order matrix of the equilibrium distribution function to elevate the accuracy but diminish the error margin as possibly as we can. Based on the foregoing, we will optimize the lattice Boltzmann model of Maxwell Equations.