Leotta, Fabio (2022)
Piecewise Parabolic Interface Reconstruction from Volume Fractions on Unstructured Polyhedral Meshes.
Technische Universität Darmstadt
doi: 10.26083/tuprints-00021080
Masterarbeit, Erstveröffentlichung, Verlagsversion
Kurzbeschreibung (Abstract)
An interface & curvature reconstruction method on unstructured meshes is presented by generalizing the ideas and efforts expressed in a previous work (cf. Kromer et al. [4]) the author has contributed to. Herein, a novel piecewise linear interface (re-)construction method, henceforth referred to as PLIC, has been proposed, whose concept is extended to accommodate a piecewise parabolic interface (re-)construction method, abbreviated as PPIC. Analogously to PLIC, the overall strategy will be to fit a paraboloid to the volume fraction data in a least-squares sense. The resulting error sum is then read as a function that is parametrized by the paraboloids base point, orientation and curvature, which allows to apply the Reynolds transport theorem to retrieve derivative information for a Newton-type minimization scheme. As it was vital to PLIC, the optimization problem that amounts to PPIC will be complemented by suitable constraints to account for volume conservation and stability.
| Typ des Eintrags: | Masterarbeit |
|---|---|
| Erschienen: | 2022 |
| Autor(en): | Leotta, Fabio |
| Art des Eintrags: | Erstveröffentlichung |
| Titel: | Piecewise Parabolic Interface Reconstruction from Volume Fractions on Unstructured Polyhedral Meshes |
| Sprache: | Englisch |
| Referenten: | Bothe, Prof. Dr. Dieter ; Kromer, Dr. Johannes |
| Publikationsjahr: | 2022 |
| Ort: | Darmstadt |
| Kollation: | III, 39 Seiten |
| DOI: | 10.26083/tuprints-00021080 |
| URL / URN: | https://tuprints.ulb.tu-darmstadt.de/21080 |
| Kurzbeschreibung (Abstract): | An interface & curvature reconstruction method on unstructured meshes is presented by generalizing the ideas and efforts expressed in a previous work (cf. Kromer et al. [4]) the author has contributed to. Herein, a novel piecewise linear interface (re-)construction method, henceforth referred to as PLIC, has been proposed, whose concept is extended to accommodate a piecewise parabolic interface (re-)construction method, abbreviated as PPIC. Analogously to PLIC, the overall strategy will be to fit a paraboloid to the volume fraction data in a least-squares sense. The resulting error sum is then read as a function that is parametrized by the paraboloids base point, orientation and curvature, which allows to apply the Reynolds transport theorem to retrieve derivative information for a Newton-type minimization scheme. As it was vital to PLIC, the optimization problem that amounts to PPIC will be complemented by suitable constraints to account for volume conservation and stability. |
| Status: | Verlagsversion |
| URN: | urn:nbn:de:tuda-tuprints-210800 |
| Sachgruppe der Dewey Dezimalklassifikatin (DDC): | 500 Naturwissenschaften und Mathematik > 510 Mathematik 500 Naturwissenschaften und Mathematik > 530 Physik 600 Technik, Medizin, angewandte Wissenschaften > 620 Ingenieurwissenschaften und Maschinenbau |
| Fachbereich(e)/-gebiet(e): | 04 Fachbereich Mathematik 04 Fachbereich Mathematik > Numerik und wissenschaftliches Rechnen |
| Hinterlegungsdatum: | 23 Jun 2022 12:03 |
| Letzte Änderung: | 24 Jun 2022 11:10 |
| PPN: | |
| Referenten: | Bothe, Prof. Dr. Dieter ; Kromer, Dr. Johannes |
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