Viscously damped acoustic waves with the lattice Boltzmann method

Acoustic wave propagation in lattice Boltzmann Bhatnagar-Gross-Krook simulations may be analysed using a linearization method. This method has been used in the past to study the propagation of waves that are viscously damped in time, and is here extended to also study waves that are viscously damped in space. Its validity is verified against simulations, and the results are compared with theoretical expressions. It is found in the infinite resolution limit k -> 0 that the absorption coefficients and phase differences between density and velocity waves match theoretical expressions for small values of omega tau(nu), the characteristic number for viscous acoustic damping. However, the phase velocities and amplitude ratios between the waves increase incorrectly with (omega tau(nu))(2), and agree with theory only in the inviscid limit k -> 0, omega tau(nu) -> 0. The actual behaviour of simulated plane waves in the infinite resolution limit is quantified.