Comparison of the Lattice Boltzmann Method and the Artificial Compressibility Method for Navier–Stokes Equations

This paper compares in detail the lattice Boltzmann method and an isothermal Navier–Stokes method. It is found that these two methods are closely related to each other. Both methods satisfy similar macroscopic governing equations in their continuous forms, but they differ from each other in their discrete forms. Besides the obvious differences in stencils for spatial discretization, these two methods also differ from each other in temporal discretization. Numerical tests show that these differences have little impact on the simulation of velocity fields but do generate noticeable differences in the pressure fields. Both methods are capable of simulating transient flows and exhibit oscillatory behavior due to the propagation of pressure waves. The lattice Boltzmann method may be more accurate for capturing the pressure waves.