A Self-Adjoint Scalar Flux Equation for Calculating Point-Source Uncollided Flux Moments Without Ray Effects
Bibliographic record
Abstract
The discrete ordinates (SN) method is one of the most popular approaches for discretizing the Boltzmann transport equation in angle. However, it comes with several disadvantages, one of them being ray effects. One of the most popular methods for mitigating ray effects is to split the angular flux into a collided and uncollided component, solving the uncollided component with a method that does not exhibit ray effects and the collided component with the SN method.This work presents a self-adjoint scalar flux (SASF) equation for computing point-source uncollided flux moments based on another recently developed advection-reaction equation, where neither of these techniques are susceptible to ray effects. The numerical results for a series of example problems in two-dimensional (2D) flatlands are provided to investigate the accuracy and rate of convergence of this technique. The SASF equation discretized with linear Lagrange basis functions was found to exhibit a second-order rate of convergence for triangular elements, and a greater than second-order rate of convergence for quadrilateral elements.These numerical experiments were followed by a three-dimensional (3D) demonstration problem that makes use of a modified form of the third Kobayashi benchmark. The structured nature of the error from the SASF equation applied to these test problems motivated the use of adaptive mesh refinement (AMR) to reduce error in both the 2D shielding and 3D Kobayashi-like problem. The results of this work showed that the SASF equations with AMR are a viable alternative to ray tracing when solving for the uncollided flux distribution from point sources with discontinuities in the total cross section of less then 10 cm−1, as larger discontinuities yielded spurious oscillations in the uncollided scalar flux.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".