SIX BOUNDARY ELEMENTS PER WAVELENGTH: IS THAT ENOUGH?

Abstract

The commonly applied rule of thumb to use six (linear) elements per wavelength in linear time-harmonic acoustics is discussed in this paper. In a survey of related work, rules of element design in computational acoustics are collected. This is followed by a brief review of the boundary element method and a more detailed presentation of boundary element interpolation functions. Constant, bilinear and biquadratic interpolation polynomials are used on triangular and quadrilateral elements. In the investigation of a long duct, the numeric solution of the three dimensional problem is compared with the analytic solution. The performance of triangular and quadrilateral, constant, bilinear and biquadratic elements is compared. The error of the numeric solution is calculated in the maximum norm and the Euclidean norm on the surface and at internal points. It is estimated how many elements per wavelength are required to remain below certain error bounds of the sound pressure magnitude. Finally, a sedan cabin compartment is analyzed using different meshes. Again, performance of constant, bilinear and biquadratic elements is discussed.