Lattice BGK simulation of sound waves

Abstract

We consider the application of the lattice Boltzmann BGK model to simulate sound waves in situations where the density variation is small compared to the mean density. Linear sound waves are simulated in two different situations: a plane wave propagating in an unbound region; and a wave in a tube. For both cases the behaviour of the simulated waves is found to be in good agreement with analytic expressions. Non-linear sound waves are also simulated and are seen to display the expected features.

Comparison between lattice Boltzmann method and Navier–Stokes high order schemes for computational aeroacoustics

“…Recently, the lattice Boltzmann method [6,21], has been studied for aeroacoustic purposes [4,7,24]. The main advantage of such a method is its ability to approximate the weakly compressible 3D Navier-Stokes equations with a simple algorithm, which is well suited for parallel computing.…”

“…The lattice Boltzmann method is based on statistical mechanics and relies on microscopic quantities instead of macroscopic ones. It has been shown [7,20,21,24] that the lattice Boltzmann model is a second order scheme that could provide good qualitative results [4,24,31]. This must be pointed out because a second order scheme is theoretically unadapted for CAA requirements.…”

Simulation of ultrasonic-driven gas separations

“…The detailed density, pressure, velocity, temperature, and species concentration distributions are calculated as a function of time. These methods have been used to model both linear and nonlinear wave propagation, 14,15 Rayleigh and Eckart acoustic streaming, 16,17 and the acoustic force on suspended particles. 18,19 The single particle distribution function f͑x , v , t͒ is the probability of finding particles at position x with velocity u at time t. The Boltzmann equation describes the evolution of the distribution function…”

Viscously damped acoustic waves with the lattice Boltzmann method

“…Spatially damped waves occur whenever a wave is radiated from an acoustic source in an absorbing medium, and is the type commonly encountered in nature. Early numerical studies of wave propagation with the LBM focused on temporally damped waves, propagating a single wavelength in a periodic system [8]. Later numerical studies have taken spatial damping into account as well [9].…”