关键词: 贝纳德对流, 纳维斯托克斯方程, 有限差分法, 格子玻尔兹曼方法

Abstract: A common phenomenon of fluid self-organization named Bernard convection is often difficult to predict，

the paper starts from the dissipative structure，then studies and simulates the Bernard convection under specific

boundary conditions by means of hydrodynamics. First of all，according to the continuity equation，energy conservation

equation and Navier-Stokes equation of incompressible fluid，Boussinesq approximation and flow function

method are introduced to simplify the control equation of Bernard convection. Because of the nonlinearity of the equation，

combined with the boundary conditions of ideal fluid，variable separation is carried out for the obtained equation，

and Lorentz system and Rayleigh number are introduced to describe the governing equation of the fluid.

Secondly，the finite difference method is used to solve the control equation of Bernard convection，analyze the

phase space trajectories corresponding to different parameters，and give the transition temperature of Bernard convection

under certain conditions. Finally，based on the lattice Boltzmann method to deal with the interaction

between the micro elements of the fluid，combining with appropriate boundary conditions，the volume of 0.008l cubic

meter three-dimensional container is divided into 106 small cubes according to the normal cube to verify the feasibility

of this method by analyzing simulation of Bernard convection.

Key words: Bernard convection, Navier-Stokes equation, finite difference method, lattice Boltzmann method