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Investigations of a Discrete Velocity Gas


Goldstein, David Benjamin (1990) Investigations of a Discrete Velocity Gas. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/DK4P-AK28.


A new model of molecular gasdynamics with discrete molecular velocity components has been implemented for parallel computation. When the suitably normalized velocity components can take only integer values and time is discretized for digital computation, the particles travel between a regular array of points in physical and velocity space, and the gas is called a "lattice gas." Calculations of molecular motions are thereby simplified. The outcome of binary collisions between particles is determined by reflections about axes of symmetry in the center-of-mass frame of reference. The procedure speeds calculations of collisions. Of interest is the insight the discrete model provides into complex physical behavior and the effect that physically realistic simplifications have on the accuracy and speed of parallel calculations of a flow.

The equilibrium state of a discrete-velocity gas and the influence of limited velocity resolution are explained. It is found that the equilibrium velocity distribution functions of the present model agree with those of the discrete Boltzmann equation at very low velocity resolution and the continuous-velocity Boltzmann equation at higher velocity resolution. The time development of non-equilibrium velocity distribution functions is presented. The model is applied to unsteady flows involving strong shock waves, heat transfer between solid surfaces, and unsteady shear layer development.

When the model is applied to gas mixtures, numerical experiments show that the required number of values of each component of molecular velocity depends strongly upon the mass ratios of the particle species involved. However, fewer than ten values of each velocity component are necessary to produce results of satisfactory accuracy in calculations of a shock wave in a single species gas. A unique, self-adaptive mesh for parallel computation, used either for the present lattice gas model or earlier direct simulation Monte Carlo (Bird, 1976) models, is described. The mesh balances the load between the processors of the multicomputer and maintains the cell size at approximately a fixed number of local mean free paths throughout the flow field.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Discrete Velocity Gas Dynamics; Discrete Velocity Boltzmann Equation; DSMC; Direct Simulation Monte Carlo Method Parallel DSMC
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Aeronautics
Minor Option:Planetary Sciences
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Sturtevant, Bradford
Thesis Committee:
  • Sturtevant, Bradford (chair)
  • Culick, Fred E. C.
  • Broadwell, James E.
  • Hornung, Hans G.
  • Seitz, Charles L.
Defense Date:27 October 1989
Non-Caltech Author Email:david (AT)
Record Number:CaltechETD:etd-05152007-093505
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1820
Deposited By: Imported from ETD-db
Deposited On:23 May 2007
Last Modified:11 Feb 2022 21:29

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