Study On The Acoustic Prediction Based On Meshless Methods

With the improvement of computer performance,the research on acoustic numerical calculation technology has been developed rapidly.The numerical calculation methods can not only solve the problems that can not be solved by theoretical analysis,but also effectively guide the experiment analysis of acoustic problems.Numerical methods have been widely used in acoustic analysis and optimization design.For example,finite difference method,finite element method,boundary element method and so on,have been widely used in the field of acoustic simulation.However,the numerical simulation methods based on mesh are dependent on the grid and the time required for the characterization of complex geometric models require meshing,which limits the practical application of the project.Meshless methods break through the limit of traditional numerical method based on meshing and have been gradually applied to the field of acoustic computation in recent years.In view of the unique advantages of radial basis function in discrete data interpolation,the paper combines radial basis function with meshless collocation method and introduces it into the field of acoustic numerical calculation.The Legendre polynomials and Chebyshev polynomials are used as interpolating basis functions to investigate the characteristics of polynomial basis point interpolation shape functions and the radial basis point interpolation shape functions.The precision and stability of the collocation meshless methods with different basis functions are analyzed.In this dissertation,the collocation meshless method based on radial basis function is introduced into the solution of acoustic time-domain wave equation,including acoustic hard boundary,soft boundary and total absorption boundary,which verifies the feasibility of solving acoustic problems in time domain.The collocation meshless method has poor accuracy and stability when dealing with derivative boundaries.The radial basis function and Hermite collocation meshless method are used to deal with the common derivative boundary conditions in acoustic problems.The accuracy and stability factors affecting the radial point interpolation collocation meshless method are systematically analyzed,including the calculation of the number of distributed points in the domain,the minimum number of nodes in the wavelength,the arrangement of nodes,the wavenumbers and the shape parameters of the radial basis functions.In this paper,a new scheme of shape parameters is proposed to solve the Helmholtz equation based on Hermite-type meshless method for complex quadratic radial basis function,and applied to the Helmholtz equation with high wavenumber,which makes it possible to solve the broadband acoustic problems.In this paper,the model of pipe sound propagation and muffler are taken as the research object.The radial basis function and Hermite collocation meshless method are used to solve the internal sound field distribution.By two-dimensional acoustic propagation in the mixed boundary of the pipeline,the meshless method and finite element method in the same node model are respectively studied.The meshless method is extended to acoustic calculation of resistive muffler and resistive muffler to verify the correctness of acoustical solution of muffler with collocation meshless method.