Propagation speed, internal energy, and direct aeroacoustics simulation using lattice Boltzmann method

The validity of the lattice Boltzmann method for direct aeroacoustics simulations depends on its ability to correctly recover the equation of state of the gas and its dynamic viscosity. This paper presents a lattice Boltzmann method with two relaxation times to carry out the direct aeroacoustics simulations of a two-dimensional Gaussian sound pulse in a uniform flow over a range of Mach numbers (M) varying from 0.01 to 0.9. It is assumed that there is no shock present in the range of Mach numbers tested. A sixth-order finite-difference scheme is used to evaluate the convective term in the modeled Boltzmann equation, and a second-order Runge-Kutta scheme is used to forward march in time. Thus solved, the calculations show that the wave propagation speed (c) over the range 0.01 ≤ M ≤ 0.9, determined from the deduced equation of state and from the propagation of the pulse, are in good agreement with theoretical analysis and direct numerical simulation results obtained by solving the unsteady compressible Navier-Stokes equations using a low-dispersive and low-dissipative finite-difference scheme. The specific heat ratio (γ) for a diatomic gas is recovered correctly and so is the dependence of the internal energy on γ. Thus, the proposed lattice Boltzmann method is valid for direct aeroacoustics simulations at very low to near transonic M.