Oberlack, Martin ; Cheviakov, Alexei F. (2010)
Higher-order symmetries and conservation laws of the G-equation for premixed combustion and resulting numerical schemes.
In: Journal of Engineering Mathematics, 66 (1)
Artikel, Bibliographie
Kurzbeschreibung (Abstract)
It is shown that the set of computable local symmetries of the G-equation for flame-front propagation of premixed combustion is considerably extended if higher-order symmetries are considered. Classical point symmetries are exhaustively discussed by Oberlack et al. (Combust Theor Model 5:363–383, 2001). Further, if the flow velocity is zero, an infinite series of higher-order symmetries has been derived by Oberlack (J Calcutta Math Soc 1:41–52, 2004). Presently it is evidenced that the G-equation also admits an infinite number of higher-order symmetries for an arbitrary velocity field. Higher-order symmetries involving derivatives up to second order are computed. Geometrical and kinematic interpretations of the symmetries are given. For the special case of constant flow velocity, an infinite set of local conservation laws of the G-equation has been derived using the direct method. It is demonstrated how the derived infinite sets of local symmetries and conservation laws can be used to develop novel numerical schemes (including higher-order ones) to perform computations in practical applications involving the G-equation.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2010 |
| Autor(en): | Oberlack, Martin ; Cheviakov, Alexei F. |
| Art des Eintrags: | Bibliographie |
| Titel: | Higher-order symmetries and conservation laws of the G-equation for premixed combustion and resulting numerical schemes |
| Sprache: | Englisch |
| Publikationsjahr: | März 2010 |
| Verlag: | Springer |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Journal of Engineering Mathematics |
| Jahrgang/Volume einer Zeitschrift: | 66 |
| (Heft-)Nummer: | 1 |
| URL / URN: | http://dx.doi.org/10.1007/s10665-009-9339-2 |
| Kurzbeschreibung (Abstract): | It is shown that the set of computable local symmetries of the G-equation for flame-front propagation of premixed combustion is considerably extended if higher-order symmetries are considered. Classical point symmetries are exhaustively discussed by Oberlack et al. (Combust Theor Model 5:363–383, 2001). Further, if the flow velocity is zero, an infinite series of higher-order symmetries has been derived by Oberlack (J Calcutta Math Soc 1:41–52, 2004). Presently it is evidenced that the G-equation also admits an infinite number of higher-order symmetries for an arbitrary velocity field. Higher-order symmetries involving derivatives up to second order are computed. Geometrical and kinematic interpretations of the symmetries are given. For the special case of constant flow velocity, an infinite set of local conservation laws of the G-equation has been derived using the direct method. It is demonstrated how the derived infinite sets of local symmetries and conservation laws can be used to develop novel numerical schemes (including higher-order ones) to perform computations in practical applications involving the G-equation. |
| Freie Schlagworte: | Conservation law; G-equation; Level-set equation; Premixed combustion; Symmetry |
| Zusätzliche Informationen: | dio:10.1007/s10665-009-9339-2 |
| Fachbereich(e)/-gebiet(e): | 16 Fachbereich Maschinenbau 16 Fachbereich Maschinenbau > Fachgebiet für Strömungsdynamik (fdy) Exzellenzinitiative Exzellenzinitiative > Exzellenzcluster Zentrale Einrichtungen Exzellenzinitiative > Exzellenzcluster > Center of Smart Interfaces (CSI) |
| Hinterlegungsdatum: | 24 Aug 2011 18:14 |
| Letzte Änderung: | 18 Feb 2019 14:58 |
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