Abstract
This paper presents an improved form of the convected Boundary Element Method (BEM) for axisymmetric problems in a subsonic uniform flow. The proposed formulation based on the axisymmetric Convected Helmholtz Equation (CHE) and its fundamental solution that describes the sound radiation from a monopole source. The variables in the new axisymmetric boundary integral formulation can be expressed explicitly in terms of the acoustic pressure and its particular normal derivative. Also, the constant coefficients are expressed only in terms of the axisymmetric convected Green's function and its convected normal derivative. The particular and convected derivatives reduce the flow effects of the normal and the flow direction derivatives incorporated in the conventional convected boundary integral formulas. The advanced form of the axisymmetric boundary integral representation with flow is a similar form of the axisymmetric boundary element method without flow. Precisely, the two new operators significantly reduce the computational burden of the classical BEM and then becomes the CPU time of BEM without flow. The formula is verified comparing to both analytical and Finite Element Methods (FEM) of an axisymmetric infinite rigid duct in a subsonic uniform flow.
Highlights
The numerical studies of some acoustic problems with fluid flow require only the special methods, such as the computational techniques of the Finite Element Method (FEM) and boundary element method (BEM) for solving any axisymmetric medium in the science and engineering
The axisymmetric Finite Element Method is based on the weak variational formulation, which can be obtained by multiplying the axisymmetric wave Equation (1) by a test function p∗
This is because the improved form of the axisymmetric boundary integral representation Equation (23) with the mean flow is similar to the boundary element method without flow
Summary
The numerical studies of some acoustic problems with fluid flow require only the special methods, such as the computational techniques of the Finite Element Method (FEM) and boundary element method (BEM) for solving any axisymmetric medium in the science and engineering. The finite element method is currently the most widely used numerical method for solving the interior medium with mean flow and that the boundary element method is used for solving the exterior medium with a constant flow [1]. It is known that the finite element method has its limitations in modeling infinite domains. Using the boundary element method (BEM), which requires a discretization of only the generator of the acoustic domain and that this Sommerfeld condition is automatically
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