Lagrangian Meshfree Particle-based Computational Acoustics for Two- dimensional Sound Propagation and Scattering Problems

Meshfree particle method, which is always regarded as a pure Lagrangian approach, is easily represented complicated domain topologies, moving boundaries, and multiphase media. Solving acoustic problems with the mesfree particle method forms a branch of the acoustic wave modeling field, namely, particle-based computational acoustics (PCA). The aim of this paper is to improve the accuracy of using the PCA method to solve two-dimensional acoustic problems, and realize the particle representation with a hybrid meshfree and finite-difference time-domain (FDTD) method for acoustic boundary conditions at both the plane and curved surface. As a widely used Lagrangian meshfree method, the smoothed particle hydrodynamics (SPH) based on the support domain and the kernel function has developed rapidly in recent years. The traditional SPH method is easily implements parallel processing and has been applied in sound wave simulation. As a corrective method with higher accuracy than SPH, the acoustic propagation and scattering in the time domain is simulated with the corrective smoothed particle method (CSPM). Moreover, a hybrid meshfree-FDTD boundary treatment technique is utilized to represent different acoustic boundaries in the Lagrangian approach. In this boundary treatment technique, the parameter value of virtual particles is obtained with the FDTD method, which concerns truncation errors based on the Tayler series expansion. Soft, rigid, and Mur’s absorbing boundary conditions are developed to simulate sound waves in finite and infinite domain. Results of modeling acoustic propagation and scattering show that CSPM is accurate and convergence with exact solutions, and different acoustic boundaries are validated to be effective in the computation.