A boundary integral formulation for two-dimensional acoustic radiation in a subsonic uniform flow

Abstract

This paper presents a new boundary integral formulation for two-dimensional acoustic radiation in a uniform subsonic flow in which the Green’s function automatically incorporates the convective effect. The integral equation representation is derived in detail, and shown to incorporate the Sommerfeld radiation condition at infinity. The order of singularities in the integrals is also analyzed. The resulting integral equation involves the derivative of the velocity potential in the flow direction; thus an approximation is necessary to express this extra variable in terms of the potential and its normal derivative. Numerical results are included to verify the formulation.

Alternative time-marching schemes for elastodynamic analysis with the domain boundary element method formulation

“…Formulations that use the static fundamental solution can be classified, according to the maintenance or not of the inertial domain integral in the BEM equations, as: D-BEM, that keeps the domain integral (D means domain) in the equations, e.g., Carrer and Telles (1994) and Hatzigeorgiou and Beskos (2001), and DR-BEM (DR means Dual Reciprocity), that by means of suitable interpolation functions substitutes the domain integral by boundary integrals, e.g., Kontoni and Beskos (1993) and Partridge et al (1992). Formulations based on frequency and Laplace domains are also available, e.g., Manolis (1983) and de Lacerda et al (1996). More recently, a formulation based on the Operational Quadrature Method appeared in the literature, e.g., Gaul and Schanz (1999) and Schanz (2001).…”

Coupling boundary elements to a raytracing procedure

“…Another effective numerical tool for the solution of acoustical problems is the boundary element method (BEM) [13][14][15][16]. Formulations of the BEM to study sound propagation in a uniform flow are presented in [17][18][19]. More recently, a promising development is the so-called fast boundary element algorithm capable of enhancing the performance of BEM significantly (see e.g.…”

Acoustic Analogy Formulations Accelerated by Fast Multipole Method for Two-Dimensional Aeroacoustic Problems

“…Equation (2) can be rewritten as the Helmholtz equation after a Prandtl-Glauert transformation; then, the Green's function can be obtained, as shown by Lacerda et al [8], as…”

“…The wideband MLFMM presented here applies a plane-wave expansion formulation [4,5] for calculations in the high-frequency regime and a partial-wave expansion formulation [5,6] in the low-frequency regime. The method is described in detail for the solution of a two-dimensional (2-D) Green's function that incorporates convective effects [7,8]. Although the method developed in this paper is applied for 2-D dipole and quadrupole integrations, it can be easily extended to accelerate 2-D surface integrations of monopole and dipole source terms, as well as 3-D volume integrations of quadrupole source terms.…”