Investigation of a lattice Boltzmann model with a variable speed of sound

Abstract

A Lattice Boltzmann model is considered in which the speed of sound can be varied independently of the other parameters. The range over which the speed of sound can be varied is investigated and good agreement is found between simulations and theory. The onset of non-linear effects due to variations in the speed of sound is also investigated and good agreement is again found with theory. It is also shown that the fluid viscosity is not altered by changing the speed of sound.

Investigation of non-linear acoustic losses at the open end of a tube

“…37 It has also been shown to be suitable for simulating acoustic waves at low Mach number. [38][39][40][41][42][43][44][45][46] A brief description of the LBM relevant to the simulations presented here is given below. A wider discussion of the LBM is available in Refs.…”

Lattice Boltzmann method for adiabatic acoustics

“…Li et al [14] resorted to a finitedifference implementation to circumvent the difficulties. Buick & Cosgrove [15] *Author for correspondence (xiaowen@exa.com).…”

A lattice Boltzmann model for two‐dimensional sound wave in the small perturbation compressible flows

“…Additionally, lattice Boltzmann models have been developed to simulate linear and nonlinear partial differential equations such as the Burgers equation [9,10], the KdV equation [11], the Lorenz equations [12], the Schrödinger equation [13][14][15], and the Poisson equation [16,17]. On the other hand, there are many significantly refined lattice Boltzmann models for the wave motion [18][19][20], shallow water wave [21], wave propagation in plasmas [22], gravity-capillary internal wave [23], acoustic wave [24][25][26][27], and light wave propagation [28,29].…”

“…However, the strategy selected is not to simulate the wave equation directly by employing the LBM for wave equation [18][19][20][24][25][26][27]. Because the equation for wave cannot reflect the information about all the physical quantities, such as density, pressure, velocity of flows, etc., the properties for sound wave but not for wave in another form may be lost, such as the conservation of entropy in the gas flows.…”