Analytical and Numerical Problems Associtated with Extending the Use of the Second order Even-parity Transport Equation.
Abstract
The purpose of this research was to determine the feasibility of extending the use of the even-parity form of the Boltzmann Equation (EPFBE) to complex linear transport problems. Previous applications had been limited to problems involving simple geometry and low order scatter approximations. The air-over-ground problem was selected for this more complex extension since it required two-dimensional cylindrical geometry, anisotropic scatter, and a multigroup solution. To eliminate the ray effect in this problem, both the finite element and synthesis method were used. With these methods the Galerkin and collocation numerical techniques were applied. The Galerkin method proved infeasible because the integrals that resulted could not be efficiently evaluated either numerically or analytically. The collocation method allowed the analytic evaluation of all derivative and integral operations, but forced a fixed anisotropy on the solution. The multigroup method applied to the EPFBE produced a nested integral problem that increased proportionately with the number of energy groups. This research demonstrated that the finite element method can not be cost effectively used in solving the EPFBE for transport problems requiring complex geometries, anisotropic scatter, and a multigroup method. Criteria developed during this research for pursuing future work with the EPFBE is presented. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1981
- Accession Number
- ADA100801
Entities
People
- John C. Souders Jr
Organizations
- Air Force Institute of Technology