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Piecewise Parabolic Interface Reconstruction from Volume Fractions on Unstructured Polyhedral Meshes

Leotta, Fabio (2022):
Piecewise Parabolic Interface Reconstruction from Volume Fractions on Unstructured Polyhedral Meshes. (Publisher's Version)
Darmstadt, Technische Universität Darmstadt, DOI: 10.26083/tuprints-00021080,
[Master Thesis]

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Item Type: Master Thesis
Status: Publisher's Version
Title: Piecewise Parabolic Interface Reconstruction from Volume Fractions on Unstructured Polyhedral Meshes
Language: English
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.

Place of Publication: Darmstadt
Collation: III, 39 Seiten
Classification DDC: 500 Naturwissenschaften und Mathematik > 510 Mathematik
500 Naturwissenschaften und Mathematik > 530 Physik
600 Technik, Medizin, angewandte Wissenschaften > 620 Ingenieurwissenschaften
Divisions: 04 Department of Mathematics > Numerical Analysis and Scientific Computing
Date Deposited: 23 Jun 2022 12:03
Last Modified: 04 Aug 2022 13:12
DOI: 10.26083/tuprints-00021080
URN: urn:nbn:de:tuda-tuprints-210800
Referees: Bothe, Prof. Dr. Dieter ; Kromer, Dr. Johannes
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/21080
PPN: 496579878
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