A DISCRETE ORDINATE TECHNIQUE FOR THE LINEARIZED BOLTZMANN EQUATION WITH APPLICATION TO COUETTE FLOW,

Abstract

A numerical method for the solution of the linearized Boltzmann equation of hard sphere molecules is developed here, in which approximations are made only in sense of numerical truncations. The distribution function is considered at n discrete points in velocity space, and a closed symmetric set of differential equations is developed which describe the evolution of the distribution function at each of these discrete points. The key point of the method is the approximation, by a finite sum, of the collision integral, utilizing Gauss quadrature (integration) formulas. The method is applied to the problem of linearized Couette flow of hard sphere molecules. Numerical results are obtained for the moments and for the perturbation distribution function at the discrete points. (Author)

Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1964
Accession Number
AD0604749

Entities

People

  • B. B. Hamel
  • M. Wachman

Organizations

  • General Electric

Tags

DTIC Thesaurus Topics

  • Boltzmann Equation
  • Collisions
  • Couette Flow
  • Differential Equations
  • Distribution Functions
  • Equations
  • Flow
  • Integrals
  • Mathematics
  • Molecules
  • Personal Information Managers
  • Perturbations
  • Truncation

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Fluid Dynamics.

Technology Areas

  • Space