Solution of the Boltzmann Equation Using an Energy Group Method

Abstract

A method is explored for solving the nonlocal linear Boltzmann equation by taking velocity moments while retaining the kinetic energy as an independent variable. The six-dimensional Boltzmann equation is reduced to a set of four-dimensional equations that formally resemble fluid equations. A numerical code is implemented for solving these equations. A number of schemes were tried for closing the hierarchy of moment equations. The validity and accuracy of the method has been tested by running a number of test problems for which exact solutions of the Boltzmann equation are available. These test problems all involve one-dimensional collision-free, free-streaming, which is trivial from the viewpoint of the Boltzmann equation, but which poses a severe test to the model, whose accuracy is improved by the smoothing effects of collisions. Satisfactory closure methods may have to become increasingly elaborate as more complicated situations are considered, and thus it is still not clear whether the method will be practical in treating real applications. Keywords: Boltzmann equation; Secondary electrons. (JHD)

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Document Details

Document Type
Technical Report
Publication Date
Oct 02, 1989
Accession Number
ADA213138

Entities

People

  • D. Colombant
  • M. Lampe

Organizations

  • United States Naval Research Laboratory

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Boltzmann Equation
  • Classification
  • Collisions
  • Computational Science
  • Differential Equations
  • Distribution Functions
  • Electric Fields
  • Electrons
  • Energy
  • Equations
  • Four Dimensional
  • Hierarchies
  • High Energy
  • Mean Free Path
  • Physics Laboratories
  • Shear Flow

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Systems Analysis and Design

Technology Areas

  • Microelectronics