An assessment of a mesh-based method for slab-geometry transport in stochastic materials Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/bk128d24b

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  • There exists a variety of methods to solve the radiation transport equation in stochastic materials, including the Levermore-Pomraning method and the atomic mix method, each of which is designed to replicate the results given by benchmarks with materials rearranged in a randomized fashion. While the atomic mix method is very simple to implement, the results given are less than ideal due to the assumption that the materials are mixed at the atomic level, precluding the account of larger individual pieces of a material. The Levermore-Pomraning method is often used to approximate the benchmark solutions for exponentially-distributed materials, but includes a coupling term in its differential equation that is more difficult to implement and is significantly inaccurate in optically thick and highly scattering materials. By assuming that the materials will not change within a cell, as happens in the benchmark solutions if the realizations are generated on a constant mesh, a set of differential equations can be derived that are coupled only at the cell boundaries. The analytic and then discretized equations for this method and each of the standard and benchmark methods are derived herein. Two separate methods of coupling for the mesh-based equations are shown, and their results using a variety of material parameters are compared with each of the standard and benchmark methods.
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