Direct simulation of acoustic scattering problems involving fluid-structure interaction using an efficient immersed boundary-lattice Boltzmann method

Abstract

An efficient immersed boundary-lattice Boltzmann method (IB-LBM) is applied to carry out the direct simulation of acoustic scattering problems involving fluid-structure interaction. In the simulation, the lattice Boltzmann method is adopted for the fluid domain, the immersed boundary method is used to handle the fluid-structure interaction and the instantaneous fluid pressure perturbation is computed to obtain the acoustic field. Compared with the conventional IB-LBMs, a force correction technique is introduced in this method to enforce the non-slip boundary conditions at the immersed boundaries and the acoustic scattering field thus can be obtained more accurately. The study of the numerical result comparison with the conventional IB-LBMs or analytical solutions is conducted on four acoustic problems, such as acoustic radiation from a pulsing cylinder, acoustic scattering from a static cylinder with pulse, or harmonic Gaussian sources and a moving two-dimensional sedimentating particle. The better efficiency of the present method is validated.

Recent progress of lattice Boltzmann method and its applications in fluid-structure interaction

“…182 Refs. 185,186 used another simple formulation of ABC for their CAA simulations and achieved better efficiency. The perfectly matched layer (PML) is the most popular ABC approach.…”

“…Implicit-IB, UI-BB and Ghost-IB were suitable for moving boundary methods, which are up to the specifications of acoustic simulations. Cai et al 186 used force correction-based IB-LBM for acoustic scattering problems involving FSI problems. The proposed methods were validated by comparing the results for acoustic radiation from a pulsing cylinder, acoustic scattering from a static cylinder with a pulse (see Figure 19), or harmonic Gaussian sources and a moving two-dimensional sedimenting particle, with the literature.

Figure 19.Acoustic pressure contours around the static cylinder at different time stages.

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“…The proposed methods were validated by comparing the results for acoustic radiation from a pulsing cylinder, acoustic scattering from a static cylinder with a pulse (see Figure 19), or harmonic Gaussian sources and a moving two-dimensional sedimenting particle, with the literature.

Figure 19.Acoustic pressure contours around the static cylinder at different time stages. 186 The cylinder is shown by the black dot at the centre of the computational domain. Acoustic scattering of the Gaussian pulse from the cylinder is evident.

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Towards a better understanding of wall-driven square cavity flows using the lattice Boltzmann method

“…The term ( , , ) f r t  represents the distribution function, r stands for the spatial position vector, t indicates the non-dimensional time,  defines the velocity vector, a denotes the particle acceleration, D d characterizes the particle diameter, 12 F ,F and 12 , ff are the post-and pre-collision distribution functions of two fluid particles, g is the vertical component of 1 2   and d is the angle differential. The left hand side, represents the streaming term, while the right hand side, characterizes the collision term, which is an integral-differential term in essence.…”

“…Based on the work performed by previous scholars [4][5][6], the lattice Boltzmann method gradually improved to be a trustable numerical methodology. It turned out that the lattice Boltzmann method is numerically capable of solving many mathematical and physical problems, including all sorts of partial differential equations [7][8][9][10], applications such as acoustic wave phenomena [11][12], multi-phase flows [13][14], combustion [15][16], fluid mechanics [17][18], and many others.…”