A Finite Element Solution of the Transport Equation.

Abstract

Using a self adjoint form of the transport equation expressed as a variational integral, finite element equations for the one dimensional, one speed, homogeneous, time independent transport equation in slab geometry were derived and envoded in Fortran 77. The accuracy of C sub 0 and C sub 1 continuous fits was compared against an analytical solution for the case of noscatter. It was found that the C fits require an excessive amount of mesh refinement. The C sub 1 fit is very accurate, and does not appear to be computationally excessive. The finite element results were then compared, for the case of isotropic scatter, to a legendre polynomial solution, and the results of a recently developed code known as Ln. The methods accuracy was sufficiently verified with inexact scattering term evaluation. A technique of exact scattering integral evaluation is proposed that should reduce the amount of refinement required for convergence, and improve computational efficiency. Additional keywords: theses; numerical analysis; interpolation; computer programs. (Author)

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1985
Accession Number
ADA159245

Entities

People

  • F. A. Tarantino

Organizations

  • Air Force Institute of Technology

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Abstracts
  • Accuracy
  • Boltzmann Equation
  • Classification
  • Computational Fluid Dynamics
  • Computational Science
  • Computer Programs
  • Differential Equations
  • Equations
  • Finite Element Analysis
  • Geometry
  • Insensitive Explosives
  • Interpolation
  • Numerical Analysis
  • Numerical Integration
  • Partial Differential Equations
  • Scattering

Readers

  • Approximation Theory.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)