Dokument: Active Flux Methods for Hyperbolic Systems Using the Method of Bicharacteristics
| Titel: | Active Flux Methods for Hyperbolic Systems Using the Method of Bicharacteristics | |||||||
| URL für Lesezeichen: | https://docserv.uni-duesseldorf.de/servlets/DocumentServlet?id=67748 | |||||||
| URN (NBN): | urn:nbn:de:hbz:061-20241128-103711-7 | |||||||
| Kollektion: | Publikationen | |||||||
| Sprache: | Englisch | |||||||
| Dokumententyp: | Wissenschaftliche Texte » Artikel, Aufsatz | |||||||
| Medientyp: | Text | |||||||
| Autoren: | Chudzik, Erik [Autor] Helzel, Christiane [Autor] Lukáčová-Medvid’ová, Mária [Autor] | |||||||
| Dateien: |
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| Stichwörter: | Cartesian grid active flux method, Euler equations, Method of bicharacteristics, Linear hyperbolic systems | |||||||
| Beschreibung: | The Active Flux method is a third order accurate finite volume method for hyperbolic conservation laws, which is based on the use of point values as well as cell average values of the conserved quantities. The resulting method is fully discrete and has a compact stencil in space and time. An important component of Active Flux methods is the evolution formula for
the update of the point values. A previously proposed exact evolution formula for acoustics is reviewed and used to construct an Active Flux method for the two-dimensional Maxwell’s equation. Furthermore, the method of bicharacteristics is discussed as a methodology for the derivation of truly multidimensional approximative evolution operators that can be used for the evolution of point values in Active Flux methods. We study accuracy and stability of the resulting methods for acoustics and compare with the Active Flux method that uses the exact evolution operator. Finally, we used the method of bicharacteristics to derive Cartesian grid Active Flux methods for the linearised and nonlinear Euler equations. Numerous test computations illustrate the performance of these new Active Flux methods. | |||||||
| Rechtliche Vermerke: | Originalveröffentlichung:
Chudzik, E., Helzel, C., & Lukáčová-Medvid’ová, M. (2024). Active Flux Methods for Hyperbolic Systems Using the Method of Bicharacteristics. Journal of Scientific Computing, 99, Article 16. https://doi.org/10.1007/s10915-024-02462-z | |||||||
| Lizenz: |  Dieses Werk ist lizenziert unter einer Creative Commons Namensnennung 4.0 International Lizenz | |||||||
| Fachbereich / Einrichtung: | Mathematisch- Naturwissenschaftliche Fakultät | |||||||
| Dokument erstellt am: | 28.11.2024 | |||||||
| Dateien geändert am: | 28.11.2024 |
