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)
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