A Finite Element Solution of the Transport Equation.
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH SCHOOL OF ENGINEERING
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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
- Theoretical Mathematics