A Comparative Study of Three Different Bounce-Back Scheme Based Methods for a Moving Curved Solid Boundary Implementation in the Lattice Boltzmann Method

In this study we investigate three different boundary conditions which are introduced to model solid curved boundary conditions in Lattice Boltzmann method، in terms of accuracy and stability، these boundary conditions are FH Boundary condition، Mass conserving FH boundary condition and OSIF boundary condition. All of these three boundary condtions are based on standard bounce back boundary condition. In standard bounce back boundary condition those distribution functions which escape from flow domain in one time step return to the flow domain exactly with the same value in the next time step. Those boundary conditions which claim that they have optimized the bounce back boundary condition try to modify those distribution functions which return to the flow domain in order to maintain conservation of mass and momemtum. Conservation of momentum for moving boundary conditions is very essential since exactly the same momemtum of the solid body should be transferred to the fluid during movement. in this study it is shown that despite the Mass Conserving FH boundary condition and OSIF boundary condition are able to fullfil conservation of mass for non-moving solid curved boundaries but they are not able to meet conservation of momentum for moving solid curved boundaries. The results from simulating flow over a two-dimensional circular cylinder in a channel and also simulating flow over and oscillating cylinder with longitudinal oscillation show that FH boundary condition predict accurate and acceptable results compared to the results form literature. Therefore to simulate moving curved solid boundary in applicational problems، FH boundary condition can be used with confidence and the results obtained can be easily trusted.