Imposition of the no-slip boundary condition via modified equilibrium distribution function in Lattice Boltzmann method

Abstract

A novel scheme for implementation of the no-slip boundary conditions in the lattice Boltzmann method is presented. In detail, we have substituted the classical bounce-back idea by the direct velocity boundary condition specification employing geometric-based manipulation of the equilibrium distribution functions. In this way we have constructed the equilibrium density function in such a way that it imposes the desired Dirichlet boundary conditions at numerical boundary points. Therefore, in fact a kind of equilibrium boundary condition is made. This specification for general curved solid surfaces is made by means of immersed boundary concepts, but without any need to interpolating density distribution values. On the other hand, the results show that the method presents a faster solution procedure in comparison to the bounce-back scheme.