A Rapidly-Converging Alternative to Source Iteration for Solving the Discrete Ordinates Radiation Transport Equations in Slab Geometry
Doctoral thesis Jun 2000-Mar 2004
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH SCHOOL OF ENGINEERING AND MANAGEMENT
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I present a numerical technique to solve the time independent Boltzmann Transport Equation for the transport of neutrons and photons. The technique efficiently solves the discrete ordinates equations with a new iteration scheme. I call this new scheme the angle space distribution iteration method because it combines a non-linear, high angular-resolution flux approximation within individual spatial cells with a coarse angular-resolution flux approximation that couples all cells in a spatial mesh. This shown to be an efficient alternative to source iteration. The new method is implemented using the step characteristic and exponential characteristic spatial quadrature schemes. The latter was introduced in 1993 and has been shown to accurate for both optically thin and optically thick spatial meshes and to produce strictly positive angular fluxes. The discrete ordinates equations can be solved using the conventional source iteration method. However, it is well known that this method converges prohibitively slowly for optically-thick problems with regions that are dominated by scattering rather than absorption. The new scheme converges rapidly even for such problems. Numerical results show that the new scheme is reliably accurate for the problems intended, and that it is fast and efficient in use of memory. The angle space distribution iteration method is demonstrated in slab geometry, for a single energy group, using isotropic cross sections, with exponential and step characteristic spatial quadrature.
- Numerical Mathematics