The problem of simulating the hydrodynamics and the acoustic waves inside wind musical instruments such as the recorder, the organ, and the flute is considered. The problem is attacked by developing suitable local-interaction algorithms and a parallel simulation system on a cluster of non-dedicated workstations. Physical measurements of the acoustic signal of various flue pipes show good agreement with the simulations. Previous attempts at this problem have been frustrated because the modeling of acoustic waves requires small integration time steps which make the simulation very compute-intensive. In addition, the simulation of subsonic viscous compressible flow at high Reynolds numbers is susceptible to slow-growing numerical instabilities which are triggered by high-frequency acoustic modes.
The numerical instabilities are mitigated by employing suitable explicit algorithms: lattice Boltzmann method, compressible finite differences, and fourth-order artificial-viscosity filter. Further, a technique for accurate initial and boundary conditions for the lattice Boltzmann method is developed, and the second-order accuracy of the lattice Boltzmann method is demonstrated.
The compute-intensive requirements are handled by developing a parallel simulation system on a cluster of non-dedicated workstations. The system achieves 80% parallel efficiency (speedup/processors) using 20 HP-Apollo workstations. The system is built on UNIX and TCP/IP communication routines, and includes automatic process migration from busy hosts to free hosts.