Abstract
The development of computational acoustics allows the simulation of sound generation and propagation in a complex environment. In particular, meshfree methods are widely used to solve acoustics problems through arbitrarily distributed field points and approximation smoothness flexibility. As a Lagrangian meshfree method, the smoothed particle hydrodynamics (SPH) method reduces the difficulty in solving problems with deformable boundaries, complex topologies, or multiphase medium. The traditional SPH method has been applied in acoustic simulation. This study presents the corrective smoothed particle method (CSPM), which is a combination of the SPH kernel estimate and Taylor series expansion. The CSPM is introduced as a Lagrangian approach to improve the accuracy when solving acoustic wave equations in the time domain. Moreover, a boundary treatment technique based on the hybrid meshfree and finite difference time domain (FDTD) method is proposed, to represent different acoustic boundaries with particles. To model sound propagation in pipes with different boundaries, soft, rigid, and absorbing boundary conditions are built with this technique. Numerical results show that the CSPM algorithm is consistent and demonstrates convergence with exact solutions. The main computational parameters are discussed, and different boundary conditions are validated as being effective for benchmark problems in computational acoustics.
Highlights
Numerical methods have been applied to model acoustic phenomena, and the development of computational acoustics allows the simulation of sound generation and propagation in a complex environment
As a Lagrangian approach, the smoothed particle hydrodynamics (SPH) method has several advantages over the standard grid-based numerical method: (i) the numerical error generated by computing the advection is eliminated, since the advection term is included in the Lagrangian derivative; (ii) complicated domain topologies and moving boundaries are represented due to its Lagrangian property, as illustrated in recent reviews by Liu and Liu [21], Springel [22], and Monaghan [23]; (iii) the interface between different mediums can be naturally traced through the particle density, instead of using a special algorithm such as the volume-of-fluid; (iv) it is easy to implement and has a parallel processing ability, for the approximation is implemented in the local support domain instead of the whole computational domain [24,25]
We proposed the use of the SPH method to solve acoustic wave equations, and tests on the sound propagation and interference simulation were conducted [29,30]
Summary
Numerical methods have been applied to model acoustic phenomena, and the development of computational acoustics allows the simulation of sound generation and propagation in a complex environment. Wolfe [26] simulated room reverberation with sound generation and reception, based on a SPH fluid mechanics algorithm, and Hahn [27] solved the fluid dynamic equations to obtain pressure perturbations during sound propagation. Both of these works can be seen as direct numerical simulations (DNS), based on the SPH method. We proposed the use of the SPH method to solve acoustic wave equations, and tests on the sound propagation and interference simulation were conducted [29,30].
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