A low Mach compressible lattice Boltzmann model on standard lattice and simulations of gas resonant oscillations

A double-distribution function lattice Boltzmann model is construct for low Mach number compressible flow based on standard lattice and numerical studies are performed for gas resonant oscillations in a one-dimensional closed tube. The oscillating flow of the gas is generated by a piston at one end, and reflected by the other closed end. Shock waves with resonant frequency or slightly off-resonant frequencies are numerically captured. The time dependent velocity and density at various locations of the tube are presented. The predicted results are qualitatively consistent with those in the previous simulations, which demonstrate the validity of the presented model.