Analysis of iteration schemes for deterministic transport in binary Markovian mixtures Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/3f462867m

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  • The Adams-Larsen-Pomraning coupled transport model has been used to describe neutral particle transport in binary stochastic mixtures. Here, the mixing statistics are considered to be homogeneous Markovian processes. While the model is robust, the convergence behavior and efficiency of this coupled model have not been addressed. Countless iterative methods could be employed to solve the coupled model. In this study, three candidate iterative schemes are analyzed with the Fourier analysis technique. The schemes are tested and implemented with a variety of material data to observe the convergence behaviors. While two schemes appear to be stable and convergent, both can converge slowly in the presence of scattering. We develop a two-grid acceleration scheme to improve the convergence rate of the fully-implicit iteration scheme. A shape function from the high-order coupled transport equations (fine-grid) is used to collapse cross-sections for an effectively-mixed one-material transport approximation (coarse-grid). In turn, diffusion synthetic acceleration is applied to the coarse-grid transport operator in the event that the effective scattering ratio is near unity. Theoretical and computational results indicate that this two-grid acceleration technique is highly efficient and effective for improving the convergence rate.
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