Boundary conditions for lattice Boltzmann method with multispeed lattices

Boundary methods and boundary node treatments for a multispeed lattice are presented in detail for incompressible isothermal flows, which remain a challenging application of the lattice Boltzmann method. We developed a completely generic way of handling boundaries with known velocity for multispeed lattices by extending and improving the on-site boundary conditions proposed by Hecht et al. [1], which was only intended for single speed lattice. In addition, we studied two ways of treating the unknown distribution functions that span several layers of nodes, namely, the external treatment (the inner layer is the boundary) and the internal treatment (the outermost layer is the boundary). The external treatment requires the use of ghost nodes at the boundary, whereas the internal treatment relies on an interpolation technique. The external treatment is found to offer more stability than the internal treatment when an open boundary condition is involved. The improved on-site boundary method for multispeed lattices is shown to be local, second-order accurate. Numerical validation is demonstrated with classical benchmark problems, namely, lid-driven square cavity, channel, and back-step flows, at different Reynolds numbers and grid resolutions.