Kromer, Johannes ; Bothe, Dieter (2023)
Third-order accurate initialization of VOF volume fractions on unstructured meshes with arbitrary polyhedral cells.
In: Journal of Computational Physics, 475
doi: 10.1016/j.jcp.2022.111840
Artikel, Bibliographie
Kurzbeschreibung (Abstract)
This paper introduces a novel method for the efficient and accurate computation of volume fractions on unstructured polyhedral meshes, where the phase boundary is an orientable hypersurface, implicitly given as the iso-contour of a sufficiently smooth level-set function. Locally, i.e. in each mesh cell, we compute a principal coordinate system in which the hypersurface can be approximated as the graph of an osculating paraboloid. A recursive application of the Gaussian divergence theorem then allows to analytically transform the volume integrals into curve integrals associated to the polyhedron faces, which can be easily approximated numerically by means of standard Gauss-Legendre quadrature. This face-based formulation enables the applicability to unstructured meshes and considerably simplifies the numerical procedure for applications in three spatial dimensions. We discuss the theoretical foundations and provide details of the numerical algorithm. Finally, we present numerical results for convex and non-convex hypersurfaces embedded in cuboidal and tetrahedral meshes, showing both high accuracy and third- to fourth-order convergence with spatial resolution. The proposed algorithm outperforms existing methods in terms of both accuracy and execution time.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2023 |
| Autor(en): | Kromer, Johannes ; Bothe, Dieter |
| Art des Eintrags: | Bibliographie |
| Titel: | Third-order accurate initialization of VOF volume fractions on unstructured meshes with arbitrary polyhedral cells |
| Sprache: | Englisch |
| Publikationsjahr: | 15 Februar 2023 |
| Verlag: | Elsevier |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Journal of Computational Physics |
| Jahrgang/Volume einer Zeitschrift: | 475 |
| DOI: | 10.1016/j.jcp.2022.111840 |
| URL / URN: | https://www.sciencedirect.com/science/article/pii/S002199912... |
| Kurzbeschreibung (Abstract): | This paper introduces a novel method for the efficient and accurate computation of volume fractions on unstructured polyhedral meshes, where the phase boundary is an orientable hypersurface, implicitly given as the iso-contour of a sufficiently smooth level-set function. Locally, i.e. in each mesh cell, we compute a principal coordinate system in which the hypersurface can be approximated as the graph of an osculating paraboloid. A recursive application of the Gaussian divergence theorem then allows to analytically transform the volume integrals into curve integrals associated to the polyhedron faces, which can be easily approximated numerically by means of standard Gauss-Legendre quadrature. This face-based formulation enables the applicability to unstructured meshes and considerably simplifies the numerical procedure for applications in three spatial dimensions. We discuss the theoretical foundations and provide details of the numerical algorithm. Finally, we present numerical results for convex and non-convex hypersurfaces embedded in cuboidal and tetrahedral meshes, showing both high accuracy and third- to fourth-order convergence with spatial resolution. The proposed algorithm outperforms existing methods in terms of both accuracy and execution time. |
| Fachbereich(e)/-gebiet(e): | 04 Fachbereich Mathematik 04 Fachbereich Mathematik > Analysis 04 Fachbereich Mathematik > Analysis > Mathematische Modellierung und Analysis 04 Fachbereich Mathematik > Mathematische Modellierung und Analysis (MMA) |
| TU-Projekte: | DFG|TRR75|TP A7 TRR 75 Bothe |
| Hinterlegungsdatum: | 10 Jan 2023 08:24 |
| Letzte Änderung: | 07 Feb 2024 11:55 |
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