Interpolated boundary condition for lattice Boltzmann simulations of flows in narrow gaps

Several different interpolation schemes have been proposed for improving the accuracy of lattice Boltzmann simulations in the vicinity of a solid boundary. However, these methods require at least two or three fluid nodes between nearby solid surfaces, a condition that may not be fulfilled in dense suspensions or porous media for example. Here we propose an interpolation of the equilibrium distribution, which leads to a velocity field that is both second-order accurate in space and independent of viscosity. The equilibrium interpolation rule infers population densities on the boundary itself to reduce the span of nodes needed for interpolation; it requires a minimum of one grid spacing between the nodes. By contrast, the linear interpolation rule requires two fluid nodes in the gap and leads to a viscosity-dependent slip velocity, while the multireflection rule is viscosity independent but requires a minimum of three fluid nodes.