DTIC ADA100638: The Application of Finite Elements pdf

DTIC ADA100638: The Application of Finite Elements

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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

• Creator/s: Defense Technical Information Center
• Date: 3/1/1981
• Year: 1981
• Book Topics/Themes: DTIC Archive, Wills, Eze E, AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH SCHOOL OF ENGINEERING, *FINITE ELEMENT ANALYSIS, *NUCLEAR EXPLOSION SIMULATION, *ANISOTROPY, *BOLTZMANN EQUATION, ALGORITHMS, COMPUTERIZED SIMULATION, STEADY STATE, SCATTERING, TWO DIMENSIONAL, HARMONICS, THESES, MONTE CARLO METHOD, KERNEL FUNCTIONS, WEIGHTING FUNCTIONS, FORTRAN, CYLINDRICAL BODIES, RESIDUALS, GEOMETRY, EXPONENTIAL FUNCTIONS, PARITY, HEIGHT OF BURST, VARIATIONAL PRINCIPLES, SPLINES(GEOMETRY), PARTICLE TRAJECTORIES

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