NUMERICAL SIMULATIONS OF ACOUSTICS PROBLEMS USING THE DIRECT SIMULATION MONTE CARLO METHOD

Open Access
Author:
Hanford, Amanda Danforth
Graduate Program:
Acoustics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
June 25, 2008
Committee Members:
  • Lyle Norman Long, Committee Chair
  • James Bernhard Anderson, Committee Member
  • Feri Farassat, Committee Member
  • Victor Ward Sparrow, Committee Member
  • Thomas B Gabrielson, Committee Member
Keywords:
  • Direct simulation monte carlo
  • knudsen number
  • relaxation
  • absorption
  • dispersion
Abstract:
In the current study, real gas effects in the propagation of sound waves are simulated using the direct simulation Monte Carlo method for a wide range of systems. This particle method allows for treatment of acoustic phenomena for a wide range of Knudsen numbers, defined as the ratio of molecular mean free path to wavelength. Continuum models such as the Euler and Navier-Stokes equations break down for flows greater than a Knudsen number of approximately 0.05. Continuum models also suffer from the inability to simultaneously model nonequilibrium conditions, diatomic or polyatomic molecules, nonlinearity and relaxation effects and are limited in their range of validity. Therefore, direct simulation Monte Carlo is capable of directly simulating acoustic waves with a level of detail not possible with continuum approaches. The basis of direct simulation Monte Carlo lies within kinetic theory where representative particles are followed as they move and collide with other particles. A parallel, object-oriented DSMC solver was developed for this problem. Despite excellent parallel efficiency, computation time is considerable. Monatomic gases, gases with internal energy, planetary environments, and amplitude effects spanning a large range of Knudsen number have all been modeled with the same method and compared to existing theory. With the direct simulation method, significant deviations from continuum predictions are observed for high Knudsen number flows.