Quantitative evaluation of the limitations of the radiation boundary elements in the finite element code ATILA
Sinanoglou, Panagiotis A.
Baker, Steven R.
Scandrett, Clyde L.
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A quantitative evaluation of the limitations of the radiation boundary elements in the finite element code ATILA has been performed. Five three dimensional models were employed, each representing a rigid spherical solid surrounded by water. Monopolar, dipolar and quadrupolar incident spherical waves were introduced and the corresponding scattered waves were computed using the ATILA code and an exact analytical solution. The dimensionless parameters that characterize the problem are ka, kL, and kR where k is the wavenumber of sound in water, a is the radius of the scatterer, R is the outer fluid mesh radius, and L is the thickness of the fluid layer. The range of values investigated were kR = 1.5, 2.5, 4.0, ka = 0.5, 1.0, 2.0 and kL = 0.5, 1.0. For axially symmetric incident fields, the maximum normalized errors occurred at the poles and were 9%, 12%, and 6% respectively. Furthermore, the errors for monopolar and dipolar incident fields were strongly influenced by the location of the radiation boundary (kR), less so by the scatterer's radius (ka); specifically the error decreases with increasing kR andlor ka. The errors for quadrupolar incident fields do not exhibit any significant dependence on kR or ka. The errors for all the axially symmetric incident fields were not affected by variations of the element's size (kL). For non-axially symmetric incident fields, the maximum deviation occurred at the equatorial points and was less than 5.5%. Further investigation using a two-dimensional model is proposed in order to determine the range of values of ka, kL, and kR which will result in negligibly small errors.
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