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.
Just Accepted
