A ghost fluid Lattice Boltzmann method for complex geometries

A ghost fluid Lattice Boltzmann method (GF-LBM) is developed in this study to represent complex boundaries in Lattice Boltzmann simulations of fluid flows. Velocity and density values at the ghost points are extrapolated from the fluid interior and domain boundary via obtaining image points along the boundary normal inside the fluid domain. A general bilinear interpolation algorithm is used to obtain values at image points which are then extrapolated to ghost nodes thus satisfying hydrodynamic boundary conditions. The method ensures no-penetration and no-slip conditions at the boundaries. Equilibrium distribution functions at the ghost points are computed using the extrapolated values of the hydrodynamic variables, while non-equilibrium distribution functions are extrapolated from the interior nodes. The method developed is general, and is capable of prescribing Dirichlet as well as Neumann boundary conditions for pressure and velocity. Consistency and second-order accuracy of the method are established by running three test problems including cylindrical Couette flow, flow between eccentric rotating cylinders and flow over a cylinder in a confined channel.