Efficient SPH simulation of time-domain acoustic wave propagation

As a Lagrangian meshfree method, smoothed particle hydrodynamics (SPH) can eliminate much of the difficulty in solving acoustic problems in the time domain with deformable boundaries, complex topologies, or those that consist of multiphase systems. However, the optimal value of the computational parameters used in the SPH simulation of acoustics remains unknown. In this paper, acoustic wave equations in Lagrangian form are proposed and solved with the SPH method to compute the two-dimensional sound propagation model of an ideal gas in the time domain. We then assess how the numerical error is influenced by the time step, the smoothing length, and the particle spacing by investigating the interaction effects among the three parameters using Taguchi method with orthogonal array design (OAD) and analysis of variance (ANOVA). On the basis of this assessment, appropriate values for these computational parameters are discussed separately and validated with a two-dimensional computational aeroacoustic (CAA) model. The results demonstrate that the Courant number for the meshless SPH simulation of two-dimensional acoustic waves is proposed to be under 0.4, whereas the ratio of the smoothing length to the particle spacing is between 1.0 and 2.5.