An investigation into curved and moving boundary treatments in the lattice Boltzmann method

Curved boundary treatments provide a means of improving the computational accuracy of the conventional stair-shaped approximation used in lattice Boltzmann (LB) simulations. Furthermore, curved boundary treatments can be extended to the modeling of moving boundary problems simply by adding a momentum term to the bounced distribution functions at the solid surface. This study commences by investigating three conventional interpolating treatments for curved boundaries in LB problems, namely the Filippova and Hänel (FH) model [O. Filippova, D. Hänel, Grid refinement for lattice-BGK models, J. Comput. Phys. 147 (1998) 219-228], Bouzidi's model [M. Bouzidi, M. Firdaouss, P. Lallemand, Momentum transfer of a Boltzmann-lattice fluid with boundaries, Phys. Fluids 13(11) (2001) 3452-3459], and Yu's model [D. Yu, R. Mei, W. Shyy, A Unified Boundary Treatment in Lattice Boltzmann Method, AIAA 2003-0953, New York, 2003]. Previous investigations have indicated that the interpolations would break the mass conservation at the boundaries, since the inaccuracy in evaluation of the momentum transfer at boundary leads to a net mass flux. Based on this reason, a concept of the interpolation-free treatment for modeling the curved and moving boundary conditions is proposed to overcome the drawback of these interpolation-based curved boundary treatments. In present study, two interpolation-free models are then proposed, namely on-site interpolation-free (OSIF) and composite interpolation-free (CPIF) models. These proposed models are initially applied to simulate the flow in the channels containing a stationary square block positioned at various locations along the longitudinal axis. The simulations results are then compared with those obtained using the three conventional interpolating treatments. The interpolation-free models are then applied to the case of moving boundary problems in which a square block and a cylindrical block, respectively, move with a constant speed along a channel containing stationary flows. To test the Galilean effect of the proposed CPIF model, a Couette flow past the stationary square/cylinder block with the moving top/bottom walls is simulated. Overall, the numerical results show that the proposed interpolation-free curved treatment models significantly improve the accuracy of the mass flux computation near the solid surface, and thus enhance the accuracy of the momentum interaction at the moving boundaries.