Computational aeroacoustics using lattice Boltzmann model

Conventional lattice Boltzmann method (LBM) has been developed mostly for incompressible and very low Mach number flows and is limited to mono-atomic gases. This thesis proposes a one-step computational aeroacoustic methods based on LBM rather than the non-linear Navier-Stokes equations. Since the improved Boltzmann equation (BE) is linear, the computational code has a very simple structure. This thesis provides detail derivations for recovering the specific heat ratio (for diatomic gases) and the Sutherland law. The resultant equation is linear on the left hand side and can be solved using a 6 th-order compact finite difference method to evaluate the streaming term and a second order Runge-Kutta time scheme to deal with the time dependent term on the left hand side of the improved Boltzmann equation. A fourth- to sixth-order accurate scheme is required for the boundary in a DNS solution while a first-order accurate boundary scheme in the improved LBM is sufficient to give the same accuracy as the DNS solutions. The improved LBM is tested against many classical problems of aeroacoustic propagation in stationary and moving medium. These include developing acoustic, vortical and entropy pulses, speed of sound recovery and sound scattering by a vortex. All improved LBM solutions are validated against DNS results and available theoretical predictions. The comparisons show that the one-step LBM scheme can be used to accurately resolve the attempted aeroacoustic problems.