| For smoothed particle hydrodynamics(SPH)method,the influence of numerical parameters on acoustic calculation is analyzed.A variable precision-moving least squaressmoothed particle hydrodynamics(VP-MLS-SPH)method is introduced,and a method,moving least square-compact support domain-smoothed particle hydrodynamics(MLS-CSDSPH)method,is proposed to improve the computational efficiency.With SPH,VP-MLS-SPH,and MLS-CSD-SPH methods,the acoustic fields with different boundaries in the frequency domain and time domain are simulated,and the implementation method of acoustic boundary conditions based on the meshfree methods is obtained,which expands the application of the meshfree method in computational acoustics.The numerical wavenumber of SPH is obtained by Fourier transform,and its error with respect to the exact wavenumber is analyzed.In the perspective of dispersion,the relation between the particle distance and the upper limit frequency that is able to compute is analyzed,and the influence of smoothing length on the numerical dispersion error is obtained.Moreover,the theoretical basis for configuring the numerical parameters is obtained,and a simulation of sound propagation in pipes is used to validate the theories.VP-MLS-SPH meshfree method with variable accuracy,based on the moving least square,is introduced in this paper.Compared with the classical SPH method,its approximate accuracy can be changed according to numerical needs,its boundary truncation error is corrected,and its consistency is better.Besides,VP-MLS-SPH can be applied with strong form and weak form,which is easy to compute the partial difference boundaries.Based on the computation of the hyperbolic,parabolic,and elliptic equations with different boundary conditions,and the modal analysis of an acoustic cavity and a 2D solid construct,the accuracy and the feasibility of VPMLS-SPH are validated.An improved VP-MLS-SPH method in weak form,MLS-CSD-SPH,is introduced.Based on different types of shape functions,the piecewise-smooth compact-kernel function is derived in the compact support domain,this compact-kernel function is able to improve the computational efficiency of VP-MLS-SPH with SPH-kernel function.The modal analysis of a2 D acoustic cavity is used to validate the high computation efficiency.The acoustic predictions of 3D silencers with different acoustic boundaries are used to validate the effectiveness and accuracy of MLS-CSD-SPH.The perfectly matched layer(PML)for the time domain acoustic absorbing boundary condition that is appropriate for the meshfree method is introduced.The exponential time differencing algorithm is used to obtain the compact PML(C-PML)that is used in static media.Moreover,a method with time and space transform is used to obtain the general form of PML for static and arbitrary mean flow media.This general form is applied in the meshfree method to validate the absorptive effect.Combining the VP-MLS-SPH & FDTD method and the admittance fitting method to eliminate the high-frequency fake wave oscillation caused by the multi freedom broadband time-domain impedance boundary in the meshfree method.This scheme decreases the numerical error and time-step limitation caused by the linear and nonlinear terms,obtaining the stability of the multi freedom broadband time-domain impedance boundary.A 1-D time-domain impedance boundary and a 2-D grazing incidence tube liner are simulated to validate the theory. |
