A dual-scale kernel reconstruction smoothed particle hydrodynamics method for broadband acoustic dispersion...

Meshfree methods are suited to acoustic simulations involving moving interfaces and complex boundaries, such as noise from moving machinery and fluid-structure interactions. Smoothed particle hydrodynamics (SPH) provides a Lagrangian framework for such problems. However, conventional SPH accumulates numerical dispersion during long-range broadband propagation. Its kernel-gradient operator acts as a dispersive filter, producing frequency-dependent phase distortion, high-frequency attenuation, and spurious trailing oscillations. Direct assignment of broadband signals to particles may produce discontinuous pressure distributions within the source region, thereby distorting the injected waveform before propagation. This paper proposes an analytically dual-scale kernel (DSK) reconstruction operator that cancels the leading dispersion error at the operator level. Combined with the corrected smoothed particle method (CSPM), it corrects spectral dispersion and local consistency errors. A retarded-time source loading strategy with impedance matching is introduced to prevent injection-stage distortion. The framework is validated through one-dimensional long-distance propagation, two-dimensional plane wave propagation, and cylindrical-wave radiation. Results show that DSK-CSPM reduces the one-dimensional L2 pressure error by approximately a factor of 150 relative to standard SPH, brings phase velocities close to the sound speed, and incurs a computational overhead of 2.9% in the two-dimensional plane wave test. The method provides an accurate and efficient strategy for high-fidelity particle-based broadband acoustic simulation.