An acoustic radiation or scattering problem in an unbounded domain is represented by the linear wave equation for harmonic waves, the Helmholtz equation, and the Sommerfeld radiation condition. The Sommerfeld radiation condition requires only outgoing travelling waves at infinity with an amplitude which decays towards zero. For simple radiation problems, like a spherical source or a cylindrical source in an unbounded domain, analytical solutions exist. More complex problems can be solved with the Finite Element Method (F.E.M.) a 'weak formulation' of the radiation problem which introduces shape, interpolation and weighting functions. However, the conventional acoustic finite elements cannot satisfy the Sommerfeld radiation condition or even model an unbounded domain. Therefore, new acoustic elements with one direction extended to infinity have been implemented in the modular finite element program B2000: the so-called acoustic Infinite Elements. These infinite elements contain special shape functions which transform the global infinite elements to finite local elements. The interpolation functions are based on the analytical solutions for simple radiation problems so that the Sommerfeld radiation condition is satisfied and a particular choice of the weighting functions preserves the advantages of the F.E.M. A comparison of the numerical results with the analytical results for simple radiation problems show that the infinite elements perform well. This is also seen in a comparison of the numerical results with the analytical results of an eigenfrequency calculation.
|Name||Aerospace Engineering Reports|
|Publisher||National Aerospace Laboratory|
|No.||NLR-TR 96603 L|