Lattice Boltzmann Method For The Flat-plate Flow

The lattice Boltzmann method (LBM) has recently become an available method for computational fluid dynamics (CFD). Unlike conventional methods based on macroscopic continuum equation, the LBM starts from microcosmic kinetic equations, i.e. the Boltzmann equation that it determines macroscopic fluid flows. The kinetic nature brings certain advantages over conventional numerical methods, such as its algorithmic simplicity, easy handing of complex boundary conditions, and programming easily. By using parallel computation scheme in a multi-processor computer, we can easily solve a larger size of problem of the uncompressible frictionless fluid with the lattice Boltzmann method.At first, the paper introduces the history and the present status of the lattice Boltzmann method. The lattice Boltzmann equation is:Using multiple-dimensioned technique to this equation:and the Chapman-Enskog expansion, we obtain the different time scale series of equationsThen we gain the values of coefficient of the equilibrium distribution function:These coefficients areIn which D is dimension, b is the direction numbers (not include rest point), c is particle velocity.By simple algebra operation and the Chapman-Enskog expansion, and macroscopic physics conservation law to the series of lattice Boltzmann equations in different time scales,We can obtain the incompressible Navier- Stokes equations div u u0tIn this paper, we use the lattice Boltzmann method to simulate the flat-plate flow in two-dimension straight pipe at the different Reynolds number. By programming to the scheme, we gain the streamlined figures and vortex- line figures. At certain Reynolds number, we obtain a series of vortexes, which is called Karman vortex street. These numerical simulation results agree well with classical ones.