[Article] Artificial Compressibility Method and Lattice Boltzmann Method: Similarities and Differences

Both the artificial compressibility method and the lattice Boltzmann method yield the solutions of the incompressible Navier-Stokes equations in the limit of the vanishing Mach number. The inclusion of the bulk viscosity is one of the reasons for the success of the lattice Boltzmann method since it removes quickly the acoustic mode, which inevitably appears as the compressible effect, and contributes to the reinforcement of the stability. In the present paper, the robustness of the artificial compressibility method is enhanced by introducing a new dissipation term, which makes high cell-Reynolds number computation possible. The increase of the stability is also confirmed in the linear stability analysis; the magnitude of the eigenvalues for high wave numbers and low resolution are drastically reduced. Comparisons are made with the lattice Boltzmann method. It is confirmed that the fortified ACM is more robust as well as more accurate than the lattice Boltzmann method.