1,721,001 research outputs found
Convergence analysis of the angular-dependent rebalance iteration method in X-Y geometry
No full textRecently, the angular dependent rebalance (ADR) method was developed for acceleration of the scattering source iteration (SI) and applied to various spatial differencing schemes of the discrete ordinates transport method in one- and two-dimensional geometries. In ADR, the lower-order equation is derived by integrating the rebalance form of the discretized transport equation over a coarse angular space. As a result, the lower-order equation resembles the transport equation, and the ADR method can be very easily implemented for various numerical transport methods in general geometry. However, it is difficult to theoretically analyze the stability of the ADR method since the ADR method is nonlinear. The authors study the convergence properties of the ADR iteration method via Cefus and Larsen`s approach (linearization and Fourier analysis) for step characteristic (SC) and constant-constant (C-C) spatial differencing schemes in infinite homogeneous X-Y geometry. The results show that the ADR method is unconditionally stable in such an ideal situation, giving confidence in the observed stability in finite heterogeneous problems
An analytic solution method for discrete ordinates transport equations in slab geometry with no spatial truncation error
No full textRecently, some authors have devised exact methods with no spatial truncation error for solving the slab geometry discrete ordinates problems. First, Barros and Larsen developed the spectral Greens function (SGF) method where an exact relation between cell-edge and cell-average angular fluxes is derived by using a spectral analysis (i.e., obtaining eigenfunctions). Second, a direct method was developed by using the Laplace transform. More generally in continuous angle, the Fourier transform and inversion were used to provide analytical benchmark solutions. While motivated by Ref. 1, the authors present a new method that gives exact solutions (with no spatial truncation error) of the one-group discrete ordinates transport equations in slab geometry. The method is based on the infinite medium Greens function (IMGF) and Placzeks lemma. The IMGF is derived analytically by spectral analysis. The method yields concise equations resulting in an economical algorithm. The method does not require a set of intermediary parameters that are used in the SGF method and should be solved numerically from a system of linear equations. The unknowns are cell-edge angular fluxes in the present method, whereas in the SGF method there are two types of unknowns: cell-edge and cell-average angular fluxes. In addition, the present method easily allows the source to be distributed arbitrarily in space. Once the final equation for cell-edge angular fluxes is solved, the analytic solution is easily represented in terms of the cell-edge angular fluxes. The numerical results show that the method gives exact solutions of the discrete ordinates equations, independent of mesh size
An Energy Based Low Cycle Fatigue Life Prediction Model of 316L Stainless Steel at Elevated Temperature
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CRX : A Characteristic Transport Theory Code for Cell and Assembly Calculations in Reactor Core Design
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