Scattering of Sound from Point Sources by Multiple Circular Cylinders Using Addition Theorem and Superposition Technique

作者：Chen Jeng Tzong^*; Lee Ying Te; Lin Yi Jhou; Chen I Lin; Lee Jia Wei

来源：Numerical Methods for Partial Differential Equations, 2011, 27(6): 1365-1383.

DOI：10.1002/num.20583

• addition theorem
• Fourier series
• null-field integral formulation
• scattering
• superposition technique

In this study, we use the addition theorem and superposition technique to solve the scattering problem with multiple circular cylinders arising from point sound sources. Using the superposition technique, the problem can be decomposed into two individual parts. One is the free-space fundamental solution. The other is a typical boundary value problem (BVP) with specified boundary conditions derived from the addition theorem by translating the fundamental solution. Following the success of null-field boundary integral formulation to solve the typical BVP of the Helmholtz equation with Fourier densities, the second-part solution is easily obtained after collocating the observation point exactly on the real boundary and matching the boundary condition. The total solution is obtained by superimposing the two parts which are the fundamental solution and the semianalytical solution of the Helmholtz problem. An example was demonstrated to validate the present approach. The parameter study of size and spacing between cylinders are addressed. The results are well compared with the available theoretical solutions and experimental data.

• 出版日期2011-11