A model-adaptive discontinuous galerkin scheme for hierarchical moment equations in kinetic gas theory

Geratz, Matthias; Torrilhon, Manuel; Theisen, Lambert

doi:10.18154/RWTH-2026-07301

A model-adaptive discontinuous galerkin scheme for hierarchical moment equations in kinetic gas theory

Geratz, Matthias^RWTH*

2026

VerantwortlichkeitsangabePresented by Matthias Daniel Geratz

ImpressumAachen : RWTH Aachen University 2026

Umfang1 Online-Ressource : Illustrationen

Masterarbeit, RWTH Aachen University, 2025

Veröffentlicht auf dem Publikationsserver der RWTH Aachen University 2026

Genehmigende Fakultät
Fak01

Hauptberichter/Gutachter
Torrilhon, Manuel (Thesis advisor)^RWTH* ; Theisen, Lambert (Thesis advisor)^RWTH*

Tag der mündlichen Prüfung/Habilitation
2025-04-25

Online
DOI: 10.18154/RWTH-2026-07301
URL: https://publications.rwth-aachen.de/record/1039565/files/1039565.pdf

Einrichtungen

Inhaltliche Beschreibung (Schlagwörter)
curved geometry (frei) ; discontinuous Galerkin method (frei) ; hp-adaptivity (frei) ; microflows (frei) ; model-adaptivity (frei) ; moment equations (frei)

Thematische Einordnung (Klassifikation)
DDC: 510

Kurzfassung
In this thesis, we present a model- and hp-adaptive high-order DG formulation on unstructured meshes. The numerical scheme is further equipped with a general boundary condition formulation and a higher order curved geometry representation, by means of either a Lagrange or NURBS basis for the element geometry. A mortar method is employed to handle the fluxes at non-conforming interfaces. The methods are implemented in Julia, yielding a prototype research code aimed at facilitating adaptive simulations of steady-state linearized hierarchical moment equations in kinetic gas theory. Representative model problems are presented and their well-posedness is discussed. Utilizing these, the framework is verified based on empirical convergence studies. High-order convergence rates are obtained, in particular for unstructured meshes and curved boundaries with general boundary conditions. It is found that a curved geometry representation is beneficial for the stability and accuracy of the numerical scheme. The capabilities of the numerical formulation and its implementation are demonstrated by simulation of a Knudsen pump microflow. The scheme is observed to be stable and converge in the presence of local mesh, DG polynomial degree and in particular model refinement.

OpenAccess:
PDF
(zusätzliche Dateien)