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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.
Technische Universität Darmstadt
doi: 10.26083/tuprints-00021080
Master Thesis, Primary publication, Publisher's Version

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Item Type: Master Thesis
Type of entry: Primary publication
Title: Piecewise Parabolic Interface Reconstruction from Volume Fractions on Unstructured Polyhedral Meshes
Language: English
Referees: Bothe, Prof. Dr. Dieter ; Kromer, Dr. Johannes
Date: 2022
Place of Publication: Darmstadt
Collation: III, 39 Seiten
DOI: 10.26083/tuprints-00021080
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: Publisher's Version
URN: urn:nbn:de:tuda-tuprints-210800
Classification DDC: 500 Science and mathematics > 510 Mathematics
500 Science and mathematics > 530 Physics
600 Technology, medicine, applied sciences > 620 Engineering and machine engineering
Divisions: 04 Department of Mathematics > Numerical Analysis and Scientific Computing
Date Deposited: 23 Jun 2022 12:03
Last Modified: 04 Aug 2022 13:12
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/21080
PPN: 496579878
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