Half-way Bounce-back Research Articles

Test of the Possible Application of the Half-Way Bounce-Back Boundary Condition for Lattice Boltzmann Methods in Complex Geometry**The project supported by National Natural Science Foundation of China (Grant Nos 19704003, 19834070 and 19904004) and by the Foundation for University Key Teacher by the Ministry of Education of China

The way of handling boundary conditions with simple bounce-back rule in the lattice gas and lattice Boltzmann method had been considered as one of the advantage compared with other numerical schemes. The half-way bounce-back rule inherits the advantage of the bounce-back rule and improves the accuracy to the second-order on flat boundaries. In this paper, we test the possible application of the half-way bounce-back rule to the system with complex geometry. Our simulation results show that the half-way bounce-back rule is a good boundary condition in the problems without emphasis on accuracy.

STUDYING THE CONTACT POINT AND INTERFACE MOVING IN A SINUSOIDAL TUBE WITH LATTICE BOLTZMANN METHOD

The multicomponent nonideal gas lattice Boltzmann model by Shan and Chen (S-C) is used to study the immiscible displacement in a sinusoidal tube. The movement of interface and the contact point (contact line in three-dimension) is studied. Due to the roughness of the boundary, the contact point shows "stick-slip" mechanics. The "stick-slip" effect decreases as the speed of the interface increases. For fluids that are non-wetting, the interface is almost perpendicular to the boundaries at most time, although its shapes at different position of the tube are rather different. When the tube becomes narrow, the interface turns a complex curves rather than remains simple menisci. The velocity is found to vary considerably between the neighbor nodes close to the contact point, consistent with the experimental observation that the velocity is multi-values on the contact line. Finally, the effect of three boundary conditions is discussed. The average speed is found different for different boundary conditions. The simple bounce-back rule makes the contact point move fastest. Both the simple bounce-back and the no-slip bounce-back rules are more sensitive to the roughness of the boundary in comparison with the half-way bounce-back rule. The simulation results suggest that the S-C model may be a promising tool in simulating the displacement behaviour of two immiscible fluids in complex geometry.

On pressure and velocity boundary conditions for the lattice Boltzmann BGK model

Pressure (density) and velocity boundary conditions are studied for 2-D and 3-D lattice Boltzmann BGK models (LBGK) and a new method to specify these conditions is proposed. These conditions are constructed in consistency with the wall boundary condition, based on the idea of bounceback of the non-equilibrium distribution. When these conditions are used together with the incompressible LBGK model [J. Stat. Phys. 81, 35 (1995)] the simulation results recover the analytical solution of the plane Poiseuille flow driven by a pressure (density) difference. The half-way wall bounceback boundary condition is also used with the pressure (density) inlet/outlet conditions proposed in this paper and in Phys. Fluids 8, 2527 (1996) to study 2-D Poiseuille flow and 3-D square duct flow. The numerical results are approximately second-order accurate. The magnitude of the error of the half-way wall bounceback boundary condition is comparable with that of other published boundary conditions and it has better stability behavior.