2016 Volume 2016 Pages 20160008
Conventional integration methods do not guarantee preservation of sound frequencies when they are applied to the sound ray equations treating the acoustic scattering by an isolated vortex. On the other hand, symplectic integration algorithms (SIAs) are known to preserve conservative quantities for long time integration. Even if it is so, results of our numerical experiments indicate that in the scattering problems, the frequency error increases substantially when the ray computed by SIA passes through the vortex core region. In order to decrease this error, a variable-time-stepping method (VTM) is introduced to the SIAs whose variation strategy is based on the estimation of vorticity of the background fluid flow. A total of nine SIAs are compared and the VTM is combined with the SIA which performs best among the SIAs considered. Proposed method, i.e., symplectic integration algorithm with variable-time-stepping method (SIA-VTM) is capable of preserving sound frequency at higher accuracy than the conventional integration methods for the scattering problems: numerical error of sound frequencies computed by SIA-VTM is approximately two-orders of magnitude smaller than the corresponding value computed by the SIA without VTM at the cost of only a slight increase in the CPU time. The scattered sound rays are computed for several model vortices.
