Pressure (density) and velocity boundary conditions inside a flow domain are studied for 2-D and 3-D lattice Boltzmann BGK models (LBGK) and a new method to specify these conditions are proposed. These conditions are constructed in consistency of the wall boundary condition based on an idea of bounceback of non-equilibrium distribution. When these conditions are used together with the improved incompressible LBGK model [1], the simulation results recover the analytical solution of the plane Poiseuille flow driven by pressure (density) difference with machine accuracy. Since the half-way wall bounceback boundary condition is very easy to implement and was shown theoretically to give second-order accuracy for 2-D Poiseuille flow with forcing, it is used with pressure (density) inlet/outlet conditions proposed in this paper and in [2] to study the 2-D Poiseuille flow and the 3-D square duct flow. The numerical results are approximately second-order accurate. The magnitude of the error of the half-way wall bounceback is comparable with that using some other published boundary conditions. Besides, the bounceback condition has a much better stability behavior than that of other boundary conditions.

No abstract

In this paper, the lattice Boltzmann equation is directly derived from the Boltzmann equation. It is shown that the lattice Boltzmann equation is a special discretized form of the Boltzmann equation. Various approximations for the discretization of the Boltzmann equation in both time and phase space are discussed in detail. A general procedure to derive the lattice Boltzmann model from the continuous Boltzmann equation is demonstrated explicitly. The lattice Boltzmann models derived include the two-dimensional 6-bit, 7-bit, and 9-bit, and three-dimensional 27-bit models. ͓S1063-651X͑97͒12512-0͔

No abstract

No abstract