Extending the applicability of implicit Monte Carlo Diffusion : frequency dependence and variance reduction using the difference formulation Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/1544br335

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  • The intent of this work is to extend Implicit Monte Carlo Diffusion (IMD)[Gen. 2001] to account for frequency dependence and to incorporate the difference formulation[Szo. 2005] as a source manipulation variance reduction technique. This work shows the derivation of the probabilities and the associated proofs which govern the frequency dependent IMD algorithm. The frequency dependent IMD code was tested using both grey and frequency dependent benchmarks. The Su and Olson semi-analytic Marshak wave benchmark was used for grey problems[Su 1996]. The Su and Olson semi-analytic picket fence benchmark was used for the frequency dependent problems[Su 1999]. The dependence upon mesh refinement was tested for both the grey and frequency dependent algorithms. This work also includes the derivation of the difference formulation as it applies to IMD. The newly derived difference formulation is then tested using aforemen- tioned benchmark problems. The effectiveness of the difference formulation is analyzed for both the grey and the frequency dependent implementations. We show that the frequency dependent IMD algorithm reproduces the Su and Olson benchmarks. The spatial refinement studies dependence indicate that while solution accuracy is not significantly compromised with coarse meshes, spatial resolution can suffer dramatically. The temporal refinement studies indicate that the existence of numerical diffusion for large time steps may require adaptive mesh refinement in time. Frequency group mesh refinement studies indicates that the computational cost of refining the frequency group structure is likely less than that of deterministic methods. This work demonstrates that applying the difference formulation to the IMD algorithm can result in an overall increase in the figure of merit for frequency dependent problems. However, the creation of negatively weighted particles from the difference formulation can cause significant instabilities in regions of the problem with sharp spatial gradiants in the solution. This will require the development of an adaptive implementation of the difference formulation to focus its use in regions that are at or near thermal equilibrium.
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