Introducing the Lagrangian approach to acoustic simulation is supposed to reduce the difficulty in solving problems with deformable boundaries, complex topologies, or multiphase media. Specific examples are sound generation in the vocal track and bubble acoustics. As a Lagrangian meshfree particle method, the traditional smoothed particle hydrodynamics (SPH) method has been applied in acoustic computation but in a quiescent medium. This study presents two Lagrangian approaches for modeling sound propagation in moving fluid. In the first approach, which can be regarded as a direct numerical simulation method, both standard SPH and the corrective smoothed particle method (CSPM) are utilized to solve the fluid dynamic equations and obtain pressure change directly. In the second approach, both SPH and CSPM are used to solve the Lagrangian acoustic perturbation equations; the particle motion and the acoustic perturbation are separated and controlled by two sets of governing equations. Subsequently, sound propagation in flows with different Mach numbers is simulated with several boundary conditions including the perfected matched layers. Computational results show clear Doppler effects. The two Lagrangian approaches demonstrate convergence with exact solutions, and the different boundary conditions are validated to be effective.
Lagrangian smoothed particle hydrodynamics (SPH) method has shown its high potential for solving acoustic wave propagations in complex domain with multi-mediums. Typical applications are sound wave propagation in speech production and multi-phase flow. For these problems, SPH with adaptive particle distribution might be more efficient, with analog to mesh-based methods with adaptive grids. If the fluid flow or moving boundary is taken into account, initially evenly distributed particles will become irregular anyway (dense somewhere and sparse somewhere else). For irregular particle distribution, conventional SPH with constant smoothing length suffers from low accuracy, phase error and instability problems. The main aim of this work is to apply variable smoothing length into SPH and apply it to 2D sound wave propagation in a domain with complex boundary. In addition, the effects of several strategies for variable smoothing length on phase error in smoothed particle acoustics are fully investigated by numerical examples and theoretical analysis. Numerical results indicate that the phase error is reduced by the use of variable smoothing length.
A Lagrangian approach for solving nonlinear acoustic wave problems is presented with direct computation from smoothed particle hydrodynamics. The traditional smoothed particle hydrodynamics method has been applied to solve linear acoustic wave propagations. However, nonlinear acoustic problems are common in medical ultrasonography, sonic boom research, and acoustic levitation. Smoothed particle hydrodynamics is a Lagrangian meshfree particle method that shows advantages in modeling nonlinear phenomena, such as the shock tube problem, and other nonlinear problems with material separation or deformable boundaries. The method is used to solve the governing equations of fluid dynamics for simulating nonlinear acoustics. The present work also tests the method in solving the nonlinear simple wave equation based on Burgers’ equation. Effects of initial particle spacing, kernel length, and time step are then discussed based on the wave propagation simulation. Different kernel functions are also evaluated. The results of numerical experiments are compared with the exact solution to confirm the accuracy, convergence, and efficiency of the Lagrangian smoothed particle hydrodynamics method.
The free overfall can be used as a simple and accurate device for flow measurement in open channels. In the past, the solution to this problem was found mainly through simplified theoretical expressions or on the basis of experimental data. In this paper, using the meshless smoothed particle hydrodynamics (SPH) method, the free overfall in open channels with even and uneven bottom is investigated. For the even bottom case, subcritical, critical and supercritical flows are simulated. For the uneven bottom case, supercritical flows with different Froude numbers are considered. The free surface profiles are predicted and compared with theoretical and experimental solutions in literature and good agreements are obtained.
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