Development of a 3D Modal Neutron Code with the Finite Volume Method for the Diffusion and Discrete Ordinates Transport Equations. Application to Nuclear Safety Analyses
Bibliographic record
Abstract
The main objective of this thesis is the development of a Modal Method to solve two equations: the Neutron Diffusion Equation and the Discrete Ordinates Neutron Transport Equation.Moreover, this method uses the Finite Volume Method to discretize the spatial variables.The solution of these equations gives the neutron flux, which is related to the power produced in nuclear reactors; thus, the neutron flux is a paramount variable in Nuclear Safety Analyses.On the one hand, the use of Modal Methods is justified because one uses them to perform instability analyses in nuclear reactors.On the other hand, it is worth using the Finite Volume Method because one uses it to solve thermalhydraulic equations, which are strongly coupled with the energy generation in the nuclear fuel.First, this thesis defines the equations mentioned above and the main methods to solve these equations.Furthermore, the thesis describes the major schemes and features of the Finite Volume Method.In addition, the author also introduces the major methods used in the Modal Method, which include the methods used to solve the eigenvalue problem, as well as those used to solve the time dependent Ordinary Differential Equations.Next, the author develops several algorithms of the Finite Volume Method applied to the Steady State Neutron Diffusion Equation.In addition, the thesis includes an improvement of the multigroup formulation, which solves problems involving upscattering and fission terms in several energy groups.Moreover, the author optimizes the algorithms to do calculations with parallel computing.The previous solution is used as initial condition to solve the time dependent Neutron Diffusion Equation.The author uses a Modal Method to do so, which transforms the Ordinary Differential Equations System into a smaller system that is solved by using the Exponential Matrix Method.Furthermore, the author developed a computationally efficient method to estimate the adjoint flux from the forward one, because the Modal Method uses the adjoint flux.Additionally, the thesis also presents an algorithm to solve the eigenvalue problem of the Neutron Transport Equation.This algorithm uses the Discrete Ordinates formulation and the Finite Volume Method.In particular, the author uses two types of quadratures for the Discrete Ordinates and two interpolation schemes for the Finite Volume Method.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".