Benchmark of no-slip boundary conditions for meshless Lattice Boltzmann Method in Stokes flow

Abstract

The introduction of the approximated streaming to the standard Lattice Boltzmann Method (LBM) decouples the space and velocity discretizations. Although many no-slip implementations knwon from LBM can be directly adopted to the models with approximated streaming, their exact behavior in the off-lattice setting remains unexplored. In this work, we investigate the meshfree off-lattice D2Q9 model equipped with several no-slip implementations -- non-equilibrium extrapolation, simple and interpolated bounceback, and moment-based boundaries -- applied to a Stokes flow around a cylinder. We compare the pressure, velocity and velocity gradient fields obtained with various no-slips, on polar and hybrid polar-scattered discretizations. We find that non-equilibrium extrapolation performs the best of all the studied no-slip realizations, giving smooth stresses and zero velocity on the solid walls. Other no-slips suffer from oscillations and/or discontinuities in the hydrodynamic fields. Hybrid discretizations are found to give higher errors than the polar grid, but improve the stability of the solution. Finally, we simulate the deformation of an elastic ring under the stresses obtained with the studied no-slips to highlight the importance of the sensible choice of the no-slip realization in more complex problems.