The application of finite elements and space-angle synthesis to the anisotropic steady state Boltzmann (transport) equation. Master's thesis

Technical Report · Sun Mar 01 04:00:00 EST 1981

OSTI ID:5549205

Wills, E E

A finite element space-angle synthesis (FESAS) solution of the steady state anisotropic Boltzmann equation in a two-dimensional cylindrical geometry was developed. Starting from a variational principle the Bubnov-Galerkin solution method was applied to the second order even parity form of the Boltzmann equation. A trial function flux expansion in bicubic splines and spherical (surface) harmonics was used. A first scatter (collision) source and an exponentially varying atmosphere were also incorporated. FESAS was developed as an alternate solution approach and an improvement in comparison to the methods of Monte Carlo and discrete ordinates. FESAS does not have the inherent characteristics which have produced the ray effect problem in discrete ordinates; also, FESAS may result in lower computational costs. The second order even parity form of the Boltzmann equation was derived and shown to be symmetric, positive definite and self-adjoint. The equivalence of a variational minimization principle and the Bubnov-Galerkin method of weighted residuals was established. The FESAS system of equations was expanded and a numerical computer solution approach was implemented.

• Research Organization: Air Force Inst. of Tech., Wright-Patterson AFB, OH (USA). School of Engineering
• OSTI ID: 5549205
• Report Number(s): AD-A-100638/6
• Country of Publication: United States
• Language: English

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