The Theory Analysis Of BGK Model And Applications In Fluid Mechanics

Lattice Boltzmann Method(LBM) is a numerical simulation method from the mesoscopic point of view which has been proposed and development very quickly since the 1990 s. The method can satisfy the continuity equation of fluid mechanics simulation and Navier- Stokes equations on the premise of guarantee the conservation of mass and momentum conservation. Compared with traditional computational fluid dynamics, the LBM has wider application fields and it can be used in debris flow, combustion, porous media, blood flow, magnetic flow and so on,in addition, the LBM is much better and simpler than the traditional SIMPLE and so on in the algorithm, it also can save more computing space, the boundary conditions of LBM can use easier rebound formats than the traditional method,it is worth noting that the LBM is suitable for large-scale parallel computing. This article mainly embarks from the theory and application study the LBM, Specific content as follows:At first, several main methods were introduced at the study of fluid mechanics,the origin of the grid LBM method, development, and the study of the basic steps of LBM also were involved. Then systematically gives a complete LBM model of conditions. And deduced the macroscopic Navier-Stokes equation from the angle of the mesoscopic, LBM is proved reasonable and reliability from two aspects of theory and examples through the compile program.Secondly, in view of the BGK model of LBM, Chapman Enskog- technology is applied in this article to analyze its error sources: the error come mainly from the compression effect of error and the error due to the grid step length, and eliminate the error by improving the density and velocity. The stability of the BGK model were analyzed at the same time, from the point of view physical,considering the BGK model is established with the expansion of the equilibrium distribution function approximation processing, makes the Boltzmann- H theorem is not completely satisfied, from the point of view of numerical algebra, BGK model equation can be viewed as discrete velocity of Boltzmann equation on the left are implicit difference,the difference of the Courant number is on the brink of Courant- Friedrichs- Lewy stability, all these caused the BGK model under certain circumstances will instability,in this paper, aiming at the condition of the equilibrium distribution function may be negative, proposes two new equilibrium distribution function, a numerical example shows that the stability of BGK model is improved.At the end of this paper, obstacles between parallel edges and heat transfer problems are numerically simulated, by flat flow around a circular cylinder, L type obstacle flow around, closed square cavity natural convection, heating the moving of the top cover four simple examples, explains phenomena mechanism from different angles, to achieve the purpose of BGK model in engineering application.