The Incident Flux Response Expansion Method for Heterogeneous Coarse Mesh Transport Problems

Mosher, Scott W.; Rahnema, Farzad

doi:10.1080/00411450600878615

Cited by 32 publications

(10 citation statements)

References 9 publications

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“…For all problems, the multigroup dependence was exactly treated while the spatial dependence was expanded in discrete Legendre polynomials [5,23] DLPs.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Here, a rather general approach is described based on expansions of the boundary conditions that couple subvolumes of the global problem, a formalism introduced as early as the work of Lindahl [4] and studied more recently by several authors [5,6,7].…”

Section: The Eigenvalue Response Matrix Methodsmentioning

confidence: 99%

“…Other related work has been development of the incident flux expansion method [5,17]. Initial work by Ilas and Rahnema focused on a variational approach using a basis of Green's functions for each variable with one-dimensional discrete ordinates [17].…”

Section: Survey Of Ermm Implementationsmentioning

confidence: 99%

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Solving eigenvalue response matrix equations with nonlinear techniques

Roberts

Forget

2014

Annals of Nuclear Energy

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This paper presents new algorithms for use in the eigenvalue response matrix method (ERMM) for reactor eigenvalue problems. ERMM spatially decomposes a domain into independent nodes linked via boundary conditions approximated as truncated orthogonal expansions, the coefficients of which are response functions. In its simplest form, ERMM consists of a two-level eigenproblem: an outer Picard iteration updates the k-eigenvalue via balance, while the inner λ-eigenproblem imposes neutron balance between nodes. Efficient methods are developed for solving the inner λ-eigenvalue problem within the outer Picard iteration. Based on results from several diffusion and transport benchmark models, it was found that the Krylov-Schur method applied to the λ-eigenvalue problem reduces Picard solver times (excluding response generation) by a factor of 2-5. Furthermore, alternative methods, including Picard acceleration schemes, Steffensen's method, and Newton's method, are developed in this paper. These approaches often yield faster k-convergence and a need for fewer k-dependent response function evaluations, which is important because response generation is often the primary cost for problems using responses computed online (i.e., not from a precomputed database). Accelerated Picard iteration was found to reduce total computational times by 2-3 compared to the unaccelerated case for problems dominated by response generation. In addition, Newton's method was found to provide nearly the same performance with improved robustness.

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“…For all problems, the multigroup dependence was exactly treated while the spatial dependence was expanded in discrete Legendre polynomials [5,23] DLPs.…”

Section: Numerical Resultsmentioning

confidence: 99%

Section: The Eigenvalue Response Matrix Methodsmentioning

confidence: 99%

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Solving eigenvalue response matrix equations with nonlinear techniques

Roberts

Forget

2014

Annals of Nuclear Energy

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“…(1.1.6). It is noted that other expansion bases may be used to treat this angular dependence [3]. The selection of basis may be best determined by optimizing for the specific solution method used to solve the resulting transport equations in the system (e.g., core).…”

Section: Project Tasks Task 11 Derive a New Multi-group Transpomentioning

confidence: 99%

Consistent Multigroup Theory Enabling Accurate Course-Group Simulation of Gen IV Reactors

Rahnema¹,

Haghighat²,

Ougouag³

2013

Self Cite

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SUMMARYThe standard multi-group method used in whole-core reactor analysis relies on energy condensed (coarsegroup) cross sections generated from single lattice cell calculations, typically with specular reflective boundary conditions. Because these boundary conditions are an approximation and not representative of the core environment for that lattice, an error, known as core environment effect, is introduced in the core solution (both eigenvalue and flux). As current and next generation reactors trend toward increasing assembly and core heterogeneity, this error becomes more significant. Additionally, the angular dependence of the coarse-group total cross section for whole-core calculation is commonly ignored. The consistent energy condensation method corrects for both effects by generating updated coarse-group cross sections on-the-fly within whole-core reactor calculations without resorting to additional cell calculations and explicitly accounting for the angular dependence of the coarse-group total cross section. The core environment effect is fully corrected by making use of the recently published Generalized Energy Condensation Theory to unfold the fine-group core flux and recondense the cross sections at the whole-core level. By iteratively performing this recondensation, an improved core solution is found in which the core environment effect has been fully taken into account. Furthermore, the energy-angle coupling effect in the coarse-group calculation is accounted for by modifying the treatment of the total cross section to include orthogonal expansions in both energy and angle. As a result, the fine-group flux can be consistently reproduced during the coarse-group calculation. This recondensation method is both easy to implement and computationally very efficient because it requires pre-computation and storage of only the energy integrals and fine-group cross sections.Moreover, the consistent generalized energy condensation method was extended to subgroup decomposition method. The subgroup decomposition method enables the cross section condensation process by preserving spectral accuracy in condensed-group transport calculations in a simpler and more direct manner, without the need for the expansion in energy. The new "group decomposition" method directly couples a consistent coarse-group criticality calculation with a set of fixed-source "decomposition sweeps" to obtain the fine-group spectrum without the need to solve for higher energy moments of the flux.Also, the subgroup decomposition method which was developed in pure transport theory has been extended to pure diffusion and hybrid quasi transport/transport theories. The culmination of the works related to subgroup decomposition method confirms that the method is in fact an acceleration technique for solving fine-group eigenvalue transport (diffusion) problems. I. PROJECT OVERVIEW Project Objective:The objective of the project is the development of a consistent multi-group theory that accurately accounts for the energy-angle coupling associated w...

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“…(84), (85) The RM method has been also implemented by Farzad and co-workers at Georgia Tech in the code COMET, but these authors have opted for the parameterization of the response matrices in terms of the eigenvalue, which introduces an approximation via the matrix interpolations. The original derivation of the RM equations was done with a variational formulation (86), (87) but was later reformulated in the simpler form given here. (88), (13) The interface angular modes are a factorized product of space, angle and energy functions, Here each face of the subdomain has been partitioned into surfaces and {pαs(r)} is a set of orthogonal polynomials on surface α; the {hm(Ω)} is a set of spherical functions on the half unit sphere and χg(E) is the characteristic function of group g. Clearly, the representation functions of lowest order, pα0(r) = 1 and h1(Ω) = 1, are constant.…”

Section: In This Expression F(i) A(i) and J+(i) -J-(i)mentioning

confidence: 99%

Prospects in Deterministic Three-Dimensional Whole-Core Transport Calculations

Sanchez¹

2012

Nuclear Engineering and Technology

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The Incident Flux Response Expansion Method for Heterogeneous Coarse Mesh Transport Problems

Cited by 32 publications

References 9 publications

Solving eigenvalue response matrix equations with nonlinear techniques

Solving eigenvalue response matrix equations with nonlinear techniques

Consistent Multigroup Theory Enabling Accurate Course-Group Simulation of Gen IV Reactors

Prospects in Deterministic Three-Dimensional Whole-Core Transport Calculations

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