Study On The Numerical Simulation Of Acoustic Problems Based On Meshless Methods

Meshless method is a new kind of numerical methods which has rapidly developed in the recent years. This method is independent of the concept of element which traditional element-type method depends on, and has the advantages that no elements are needed totally or partly, avoiding the onerous mesh generation and re-meshing, etc. The method is paid very much attention by scientists and engineers in various computational researches because of its greatly theoretical and applicable value. Radial basis function (RBF) has been used successfully in scattered data interpolation, the introduction of the RBF to the collocation method for solving partial differential equations has many advantages, such as the method is a truly meshless method, does not require any meshes, easy to implement, high accuracy, and gradually developed into a mature meshless method.The main purpose of this dissertation is to introduce the basis system of the RBF collocation meshless method into acoustics researches and develop new types of meshless methods which are suitable for the acoustics numerical simulation. Therefore, two parts of important contents are studied in details, including researches on the common theoretical problems of meshless methods themselves and the special applicable background of acoustics, especially for the analysis of computational aeroacoustics (CAA) problems.A localized RBF collocation method was proposed to solve CAA problems, the method yields the generation of a small interpolation matrix for each data center and hence circumvent the highly ill-conditioned dense matrix dute to the globally supported RBF. An upwind implementation is further introduced to contain the hyperbolic property of the governing equations by using flux vector splitting method.A boundary type RBF meshless method is presented for acoustic eigenvalue problems, in which the modified variational formulation is combined with the moving least squares (MLS), while the domain integration is interpolated by RBF. This method is a truly meshless method, and elements are not required for either interpolation or integration, only discrete nodes are constructed on the boundary of a domain, several nodes in the domain are needed just for the RBF interpolation. The numerical examples show that the accuracy and convergence of the methodare high, and the pre-processing is very easy.The propagation of acoustic waves along a duct with different air flow, different wall conditions, and different shapes of the duct cross-section is considered in this dissertation. The duct cut-off frequency and the transmission characteristics of acoustic mode are dicussed deeply. The numerical simulation on the acoustics perforces of a single cavity expansion muffler are carried by the localized RBF collocation method, including the rigid and impedance wall boundary conditions. Some studies on the transmission characteristics of acoustic mode and duct cut-off frequency are carried by the boundary-type RBF collocation method. The meshless method is finally extended to the calculation on acoustic performance of mufflers in practical engineering field. The comparision between the results obtained from the numerical method and which from the expermential shows that the meshless method can be applied to engineering pratice in the muffler design and calculation. As opposed to the traditional one-dimensional models, the use of RBF meshless method which based on three-dimensional models is more guidance for the muffler structure design.The systematic studies on the numerical simulation of acoustic problems show that, as a truly meshless method, the RBF collocation method has several advantages over the traditional methods:such as it does not need any mesh, it is an independent spatial dimension which can be easily extended to high-dimensional problems, it can also be extended to solve the partial differentional equations with higher order derivatives whithout any difficulties, and it is easy in implementation and programming. RBF collocation method will become an important method in acoustic numerical simulation because of its feasibility, effectiveness and outstanding advantages in the simulation of acoustics.