Alternative curved-boundary treatment for the lattice Boltzmann method and its application in simulation of flow and potential fields

Abstract

Since the lattice Boltzmann method originally carries out the simulations on the regular Cartesian lattices, curved boundaries are often approximated as a series of stair steps. The most commonly employed technique for resolving curved-boundary problems is extrapolating or interpolating macroscopic properties of boundary nodes. Previous investigations have indicated that using more than one equation for extrapolation or interpolation in boundary conditions potentially causes abrupt changes in particle distributions. Therefore, a curved-boundary treatment is introduced to improve computational accuracy of the conventional stair-shaped approximation used in lattice Boltzmann simulations by using a unified equation for extrapolation of macroscopic variables. This boundary condition is not limited to fluid flow and can be extended to potential fields. The proposed treatment is tested against several well-established problems and the solutions order of accuracy is evaluated. Numerical results show that the present treatment is of second-order accuracy and has reliable stability characteristics.