Analysis and development of spatial hp-refinement methods for the neutron transport equation
type: Dataset
description: The different neutronic parameters have to be calculated with a higher accuracy in order to design the 4th generation reactor cores. As memory storage and computation time are limited, adaptive methods are a solution to solve the neutron transport equation. The neutronic flux, solution of this equation, depends on the energy, angle and space. The different variables are successively discretized. The energy with a multigroup approach, considering the different quantities to be constant on each group, the angle by a collocation method called Sn approximation. Once the energy and angle variable are discretized, a system of spatially-dependent hyperbolic equations has to be solved. Discontinuous finite elements are used to make possible the development of $hp-$refinement methods. Thus, the accuracy of the solution can be improved by spatial refinement (h-refinement), consisting into subdividing a cell into subcells, or by order refinement (p-refinement), by increasing the order of the polynomial basis.In this thesis, the properties of this methods are analyzed showing the importance of the regularity of the solution to choose the type of refinement. Thus, two error estimators are used to lead the refinement process. Whereas the first one requires high regularity hypothesis (analytical solution), the second one supposes only the minimal hypothesis required for the solution to exist. The comparison of both estimators is done on benchmarks where the analytic solution is known by the method of manufactured solutions. Thus, the behaviour of the solution as a regard of the regularity can be studied. It leads to a hp-refinement method using the two estimators. Then, a comparison is done with other existing methods on simplified but also realistic benchmarks coming from nuclear cores.These adaptive methods considerably reduces the computational cost and memory footprint. To further improve these two points, an approach with energy-dependent meshes is proposed. Actually, as the …
identifier: NNT: 2011AIX10085
issued: 2026-05-29T02:21:44.667380
language: fr
modified: 2026-05-29T02:21:44.667386
contact point: Organization
  fn: CCSD
keyword: discontinuous-galerkin
keyword: equation-de-transport
keyword: error-estimates
keyword: estimateurs-derreurs
keyword: finite-volumes
keyword: galerkin-discontinu
keyword: hyperbolic-system
keyword: infoeu-reposemanticsdoctoralthesis
keyword: mathmath-apmathematics-mathanalysis-of-pdes-mathap
keyword: mathmath-namathematics-mathnumerical-analysis-mathna
keyword: neutron-transport
keyword: neutronics
keyword: neutronique
keyword: physnuclphysics-physicsnuclear-theory-nucl-th
keyword: simulation
keyword: simulation-par-ordinateur
keyword: systeme-hyperbolique
keyword: theses
keyword: transport-des-neutrons
keyword: transport-equation
keyword: volumes-finis
landing page: https://theses.hal.science/tel-00769546

Analysis and development of spatial hp-refinement methods for the neutron transport equation
type: Distribution
format: HTML
issued: 2026-05-29T02:21:44.698944
modified: 2026-05-29T02:21:44.610425
access URL: https://theses.hal.science/tel-00769546

test_moissonnage_selune
type: Agent