Smoothed Particle Hydrodynamics Method With Application To Aeroacoustics

In the process of human speech production,vocal tract dynamically and continuously changes its shape.As contents and tone of the voice depend on the shape of vocal tract,the change of which will lead to the voice change.When the flowing medium inside the vocal tract has high speed,the medium movement will also affect the sound wave propagation.Therefore,to accurately simulate sound wave propagation in vocal tract,the effects of the moving boundary and fluid flow have to be taken into account.Numerical simulation is one of the common ways to study acoustic problems.According to the discretization of governing equations,the used numerical methods include grid-based and meshless approaches.Grid-based methods are mainly the finite difference method(FDM),finite element method(FEM)and boundary element method(BEM).In these methods,the computational domain has to be partitioned with grids or nodes according to given rules.The connections between nodes have to be assigned in advance and,generally,will not change during the computation.In this paper,the Smoothed Particle Hydrodynamics(SPH)method is studied and applied to acoustic problems.As an effective meshless method,it overcomes various numerical difficulties occurred in grid-based methods due to the usage of grids or mesh,such as the high cost in mesh generation and distortion of the moving mesh.Working in the Lagrangian framework,SPH is considered to be one of the most prospective meshless methods for the simulations of complex fluids.For sound wave propagation in vocal tract,a complete mathematical model is firstly built.To reduce the numerical complexity,reasonable simplifications are then applied and the aeroacoustic wave equations in Eulerian framework are obtained.With the help of material derivative,the Euler equations in Lagrangian form are derived.After discretizations of spatial and temporal derivatives by SPH and Runge-Kutta method,respectively,the discrete Euler equations in Lagrangian particle form are then derived.To impose boundary conditions and,at the same time,remedy the boundary deficiency problem of SPH,virtual particle method is used to complete the missing kernel support truncated by system boundary.The implementation of the virtual particle method in practical calculation is detailed.To efficiently find theneighbor particles in the support domain of a particle,the link-list search algorithm is used.To verify the accuracy and effectiveness of SPH,the dam break and symmetric bending tube problems are simulated.The results have reasonable agreements with those in literature.Finally,the proposed method has been successfully applied to oneand two-dimensional acoustic problems.The results are compared with the Finite Difference Time Domain(FDTD)solutions and good agreements are observed.For aeroacoustics,the SPH solutions are validated against Doppler effect based theoretical solutions.In this thesis the capability of the meshless Lagrangian SPH method for complex aeroacoustic problems is clearly demonstrated.