Finite Difference Lattice Boltzmann Method for Incompressible Navier-Stokes Equation Using Acceleration Modification

An improved finite difference lattice Boltzmann method (FDLBM) is developed to simulate incompressible flows. The basic idea is to decrease the density fluctuation which might lead to compressible error in the flows with high pressure gradient or high speed motion. The equation of state is modified by including the attractive and repulsive forces between particles to adjust the compressibility of fluid. This effect is incorporated by applying acceleration modification which is deduced based on macroscopic dynamics. Using this method the sound speed of the fluid can be also controlled easily. Numerical simulations of steady Poiseuille flow and unsteady Womersley flow were adopted to validate our model. The results show that the proposed model is much more efficient than the conventional LBGK method when solving the incompressible flows with high pressure gradient.