A Meshfree Method For Computational Acoustics In The Time Domain And Its Applications

It is known that the meshfree method is less sensitive to grid than the traditional numerical simulation method, which can lead to a lower demand of meshing capability and also reduce the labor cost and time consumption in the process of mesh generation. In addition, the meshfree method, based on the support domain and kernel function, can get rid of the computation of the matrix on the whole computation domain, which could reduce the solving procedure of ill-conditioned matrix effectively. Due to these particular advantages, the meshfree method is widely used in various research fields. Specially, the Smoothed Particle Hydrodynamics(SPH) known as a meshfree method, has seen a rapid development in recent years, which is easy to implement and has the ability of parallel processing. However, the relevant research using the SPH to solve acoustic problems is very limited. Moreover, the development of the meshfree method is further restricted by the shortcomings of high time consumption and low precision in computation.In this paper, based on the assumption in the computational acoustics that the medium of the acoustic wave with small amplitude is uniform and quiescent, the SPH with Lagrangian property is simplified into a meshfree method, which reduces the time consumption of particle searching greatly. Meanwhile, the corrective SPH method is introduced,and thus can improve the computation accuracy. This paper first describes the wave equation of small amplitude acoustic wave, and also gives the algorithm representation of the SPH. Then, the traditional SPH method is corrected to construct a Corrective Smoothed Particle Method(CSPM) on the basis of Taylor series expansion. Additionally, the wave equation of the small amplitude acoustic wave is solved by combining the CSPM with leap-frog integration. Since the medium is uniform and quiescent in the simulation, the position of the particle does not change with time. Consequently, it only needs to perform particle searching in the first time step, which can reduce the computational time and improve the computational efficiency dramatically.On this basis, the propagation models of acoustic wave along a duct and acoustic wave of the Guassian pulse are simulated by utilizing the time domain CSPM algorithm. Then, the CSPM algorithms and codes are found to be valid by comparing the numerical simulation results with theoretical solutions. Furthermore, this paper discussed the main computational parameters in the CSPM algorithm and it is shown that the CSPM algorithm shows a very good convergence. In general, the Courant-Friedrichs-Lewy(CFL) number is preferably set as 0.2 under the condition that the computational precision and efficiency can be ensured in numerical simulation.Unfortunately, the CSPM suffers from the problem that the particles on the boundary will get lost due to the fact that the CSPM is calculated based on the support domain. Therefore, the Finite-Difference Time-Domain(FDTD) method is introduced to combine with the dummy particle technique, and thus the CSPM/FDTD hybrid method of acoustic boundary is accordingly constructed. The feasibility and validity of CSPM/FDTD hybrid method is verified by simulation the model of acoustic boundary.Finally, this paper studies the application of the CSPM method in the acoustic time domain simulation, and the sound scattering of the soft and rigid circle are simulated, respectively. In addition, by appropriately weakening the restriction of medium, this paper presents the acoustic simulation method in uniform flow field, and the computation for the sound propagation of acoustic wave in lower Mach number. By comparing with results of the existing literature, it demonstrates that the CSPM algorithm can be employed to solve engineering problems effectively, and provides an impetus for the design and improvement of structural acoustic properties.